What would the effects of firing only the gunpowder in a weapon against an opponent's body?

Duncan Drake's answer suggests one little extra possibility.

When I mention the bayonet here, bear in mind I do so 40 years after asking a Vietnam vet why anyone would ever use a bayonet and he said no one would if they still had bullets left which I've always thought made so much sense that I've not ever challenged it in my mind. (Lol, after all, it matched my thinking exactly and that's always convincing, right? But it framed the point so perfectly for understanding it.)

So, the bayonet. There you are in this world with no bullets but a loaded gun and involved in what people usually call melee combat, meaning, no guns and really meaning, no bullets. Bayonets are always presented as STABBING weapons, in any context I've ever encountered right down to WWI German overcoats apparently being designed to resist said stabs and nothing ever said about slashing. I'm sure a slash or seven would be used if one thought it helpful, but bayonets seem to be stabbing weapons.

So you stab. ANY amount of damage you do in the stab is all to the good, and will be whatever you managed to achieve. But THIS gun is loaded with a full charge, or more, of black powder (where Frank's gun (the vet, above) would have had no bullet or any kind of charge since it was meant for bullet firing). So you COULD, the moment you achieve most of your stab, fire the powder directly into the place of insertion (slightly off, but...) and do all the damage the above answers suggest, but dead on a torn open place on the body. Very close to that body and the hole just made (might fire as pulling out rather than at deepest insertion) that powerful blast would likely have much more serious effect, especially if it did successfully enter the body's interior. At the least, it seems to me the open wound might be terribly enlarged, a nice result in itself.

That might also give you some respect as a man with a "real" spear (the thing a bayoneted rifle comes closest to) or sword grins at you as if you're a dead man and closes in. Anything making such a creature hesitate or not just berserk me is good in my book.

Also consider how it could affect something like a shield. A little care if you can could have you fire right at the part opposite the holder's forearm which, if reasonably close, might even break that arm, quite reducing his effectiveness against you. Additional odd things in this category might include that you can pick your target differently than "going for a kill, always" suggests (a FINE approach, if it is available to your circumstances, but this might not be such a circumstance, so small gains ending in a dead enemy could the good thing to aim for). For example, aim at a foot or knee. The massive punch described above would seriously reduce your enemy's chances. Perhaps in the frenzied parry and thrust, you might get a chance to target the weapon-holding hand. Further, anything that impacts the eyes even partially could be devastating. All little things, desperations perhaps as the properly clad and armed enemy moves in to kill you, but could be gamechangers if they succeed. And when pointing downward, another target most can figure out might be clad in a strong metal cup, so to speak, but the hammer blow others describe could make the phrase "scraped off" apply which should take the steam out of an attacker ...

Surely such a world would see you carrying the gun, usually, as a complete extra to your own proper melee weaponry, but as Frank said, broadening the concept, not the point, you use it (gun in this case, not a bayonet, but still a definite "down the list" choice) when what you really use is not available. Perhaps why you slung it on rather than not carrying the 5-15# extra weight. Maybe an extra sword would've been a better extra, but you had a rifle, not a second sword, so...

You're just a stones throw away...

While lead bullets might be rare, it's really unlikely people couldn't find something to shoot. Some of the earliest bullets were stones (https://en.wikipedia.org/wiki/Bullet), which are dirt cheap (literally) and a lot better than firing a gun with just black powder. These aren't great, but you are talking abundant powder and a short supply of projectiles.

First of all let's stress the fact that we are talking about black powder (also named in America gunpowder) which has different properties from modern smokeless powder. Aside from smoke black powder yields much lower pressure. Bullets from this guns are subsonic while bullets from modern ammunition are often super sonic (with some being sub sonic by design).

Let's do some calculations to understand better the amount of energy that such a gun would discharge. Am not trying to be exact as there are many variables involved but just trying to get in the correct order of magnitude.
Gunpowder releases 3 megajoules per kilogram and contains its own oxidant.
Gunpowder composition and characteristics

Muzzle loading firearms are proofed using a double or even triple charge to have a safety margin.
When it comes to load for rifles most suggest either 1 grain per caliber or 1.5 grain per caliber to stay well within safe limits. But notice that pistols it’s more like .25-.5 grains per caliber. Pistols aren’t as built up as rifles.

This leads us for a .50 caliber firearm:
rifle: 50-75 grains = 3.2-4.9 grams
pistol: 12.5-25 grains = 0.80-1.6 grams

let's keep just the higher value because your raiders are mean
rifle: 4.9 grams will yield: 3 Mj * 4.9 * 10^-3 = 14.7kJ
pistol: 1.6 grams will yield 3 Mj * 1.6 * 10^-3 = 4.8kJ

To have a comparison a boxer heavy weight can punch around 1kJ with some estimates of 1.6kJ. So your pistol would produce at least three times as much as a heavy weight champion.
But then there is another, more complex, problem. How much of that energy is going to actually be delivered to the target?
Here things get more complicated because as soon as the pressure builds up the target and the shooter are being pushed apart. The energy starts being dissipated on the sides increasing the invested area but lowering the pressure and so the damage that the area is taking. Another reducing factor would be if the target surface is slanted. Further the damage on the target body will depend on any kind of protection he may be wearing.
For all these factors the energy actually delivered to the target will be lower than the stated 4.8kJ for a .50 pistol.
So while killing someone might be possible it does not look like it would happen consistently enough to use this as a fighting method where your first concern is that of stopping your foe before he can do you any harm. With a rifle you are going to achieve much more energy but it seems impractical (and dangerous) to fight someone at close quarters with just a rifle. The foe could move the muzzle to the side and stab you with the other hand. With a bayonet on the rifle you have a better fighting chance though.
Still it does not look something that has any practical advantage.

As an execution method though it may be. A long, painful method that most likely should be repeated again and again before the poor victim finally dies.

TL;DR: Use a projectile, almost anything might do at close range. And anything will provide more damage to the opponent than shooting just the powder.

If your firearms can only be used at point blank range, you need a

Captive bolt gun.

https://en.wikipedia.org/wiki/Captive_bolt_pistol

The bolt consists of a heavy rod made of corrosion-resistant alloys, such as stainless steel. It is held in position inside the barrel of the stunner by means of rubber washers. The bolt is usually not visible in a stunner in good condition. The bolt is actuated by a trigger pull and is propelled forward by compressed air, a spring mechanism, or by the discharge of a blank round ignited by a firing pin. After striking a shallow but forceful blow on the forehead of the animal, spring tension causes the bolt to recoil back into the barrel.

A captive bolt gun propels a bolt attached to the firearm. The villain in the movie No Country for Old Men used a pneumatic captive bolt gun as his weapon. Captive bolt is perfect for your people who have powder and guns but no projectile. The discharge of powder can propel a piece of metal out the front of the gun into the enemy - a better offensive use of the force than just the expanding gases.

You could have the bolt on a spring so it would retract itself for the next shot. Or maybe the user would need to replace it.

If you have absolutely nothing in the barrel apart from black powder, then, if is tamped down, you will simply blow a lot of the powder out, un-ignited. This will be followed by a short-lived flame containing sparks of still burning powder. The flame will travel a few feet, depending on the bore of the barrel and the amount of the charge.

Don't stand within 6-feet but, directly in front of the barrel you should (disclaimer) be safe at 20ft, depending on the wind direction.

How do I know? As an irresponsible young teenager I experimented with home-made guns and gunpowder. I'm very lucky I wasn't blinded or seriously burned and scarred for life. DON'T TRY TO REPLICATE ANY OF THIS, IT IS FOOLISH AND DANGEROUS. A lot of inventors were killed or maimed when guns were new technology.

You don't need bullets; anything inside the barrel will be accelerated with potentially lethal effect. Shot, scrap metal, pebbles etc. In early firearms, soldiers in the heat of battle sometimes accidentally fired their ramrod at the enemy. (Very short range, but deadly at point-blank).

Blank rounds can indeed kill. Often the problem is metal fragments from the catridge case which can travel several metres. However, the blast itself is enough to kill if pressed against the temple, as illustrated by the case of Jon-Erik Hexum, an actor who accidentally killed himself by this means -- https://en.wikipedia.org/wiki/Jon-Erik_Hexum#Death