How did Angela kill twenty men at once?

While I fully agree with Omegacron I believe that he failed to answer your question which was closer to, "how did they die because of her" not, "how was she able to kill them". Omegacron explains that it was her understanding of time, motion, heat, and energy that allowed her to kill them but not how they died. If we consider what she said I believe that there are two possible answers.

Angela said:

What is time but motion? What is motion but heat? And are not heat and energy but different names for the same thing?

First we could say that she connected time to motion, and thus to heat and energy. By doing this, she may have caused time itself to light them on fire, perhaps providing the energy required to continue the spell from the spell itself.

The second possibility assumes she connected energy, magic, to time through heat and motion. She may have spent magical energy to age them into oblivion.The amount of energy to do that would likely by large, so this seems unlikely. However, the wording of her answer seems to suggest that time was used to kill the men, which seems to be in line with Angela's odd style, making this option seem more probable.

There is, of course, no way to know for certain. But all other possible explanations would seem to violate her wording to some extent, which apparently renders these options as most likely.

Angela has a deep knowledge of things. It is possible that she understands that time is irrelevant and all that moves it is motion.

Word of God answer from Christopher Paolini:

Can you tell us what spell Angela used to kill the guards under Dras-Leona? What is time but motion? What is motion but heart?

Wibbly wobbly timey wimey.
_source

More serious Word of God answer from Christopher Paolini:

I have been wondering about the spell that Angela used to make her so fast she couldn’t be seen in the fourth book and she tells him “what is time but motion and motion heat and heat energy. “And then refuses to say anything else. Could you please elaborate?

Ha! She was essentially talking about the ability to manipulate apparent time by slowing down or speeding up the vibrations of matter. Which requires an ungodly amount of skill, energy, and understanding.
_source

It's really obvious, what she is saying is, with magic you can create heat, you can move things, you can even stop time.... She stopped time, walked up to each of the men and stabbed them precisely in the eye than returned to where she was standing.

My understanding was this. She said what is time but motion. And what is motion but heat. And heat is energy. So she meant to connect energy with time. I think what she did was using energy to manipulate time so that she was next to all the men at the same time. As in kind of like cloning herself in a way. And then stabbing them each. That blur that Eragon saw next to each men was sort of a mirage of Angela that lasted less than a fraction of a second.

I think the answer can be found in the movie "Lucy" "Time is the only thing that gives validity to matter."

Angela might have used the heat generated by the men themselves as they moved to partially isolate them for an infinitesimally small period of time from the world around them. If you consider the vast energies involved in the movement of the planet, if the men were somehow made susceptible to that movement, without the corresponding protections we all enjoy as matter resting on said planet, it might well have fatal consequences for the soldiers.

What is time but motion and what is motion but heat? And are heat and energy different not different names for the same thing?

This implies to me that she understands that as your speed approaches the speed of light, you can greatly slow time. Heat is motion on the molecular level and theoretically she could have cast a spell that transferred thermal kinetic energy to kinetic energy across her body. She also says she cant use that spell again, not without hurting herself. Accelerating this quickly, even if across your body evenly, isn't good for it... she was also exhuasted which is part of acceleration sickness.

She stabbed them—really quickly

It might seem that what Angela did is left vague, but it’s really made fairly clear. There’s an important word here that the other answers missed:

Without so much as a single cry, the twenty men stiffened and fell to the floor, dead, every last one of them.

Alarmed, Eragon slowed to a stop before he ran into the bodies. Each of the men had been stabbed through an eye, as neat as could be.

He turned to ask Arya and Angela if they knew what had happened, but the words died in his throat as he beheld the herbalist. She stood braced against a wall, leaning on her knees and panting heavily. Her skin had gone deathly white, and her hands were shaking. Blood dripped from her poniard.

_Inheritance

A poniard is a small dagger. That blood was dripping from it implies that she had just stabbed the twenty soldiers with it.

Her spiel about time, heat, energy and motion indicates that she was able to speed herself up to such an extent that time seemed to have stopped, thus allowing her to stab the soldiers with her poniard at her leisure. Presumably she did this with the heat or chemical energy from her own body, the same sort of thing that fuels all spells. As a Time Lord (or possibly former companion), she would be expected to have a good understanding of temporal matters.¹

Sadly, there was no superheated air involved.

_{1. Not a joke. She almost says Raxicoricofallapatorius at one point.}

I'm fairly sure that, in some way, she used the energy in her body to connect somehow to time via heat and motion; thus giving her the ability to basically just walk up to them and stab them. However, she seemed exhausted afterwards and said she couldn't use the spell again, showing that it requires a large amount of energy to pull off. I also believe that had she used it for longer periods of time (say, to kill every soldier in the city) the energy drain could well have killed her.

He had only covered a few feet, however, when a flicker of movement appeared next to each man: a soft, shadowy blur, like the motion of a windblown pennant seen at the edge of his vision.
Without so much as a single cry, the twenty men stiffened and fell to the floor, dead, every last one of them. Alarmed, Eragon slowed to a stop before he ran into the bodies. Each of the men had been stabbed through an eye, as neat as could be. He turned to ask Arya and Angela if they knew what had happened, but the words died in his throat as he beheld the herbalist. She stood braced against a wall, leaning on her knees and panting heavily. Her skin had gone deathly white, and her hands were shaking. Blood dripped from her poniard.

Her answer after eregon asked her how she did it was:

What is time but motion? What is motion but heat? And are not heat and energy but different names for the same thing?

I believe that she used heat from her body to make energy that she used to go super fast, according to the shadowy blur and her hands shaking. It used so much energy that she went deathly white, the speed could have also done that, making her sick, which would explain why she could only do it once. She activated the spell, walked/ran up to each man, stabbed them in the eye, went back to where she was standing, and released the spell. Another explanation is that she sent her mind/soul into another dimension that is in the same place as the earth, and stabbed them from their, and when she left she went back to her body, explaining why she did not just appear next to the men after ending the spell. It used a massive amount of energy, explaining why she was breathing heavily, and it could also explain why she could only do it once.

If anyone says that elves say that you can't make heat into energy, remember, Angela knows more then the elves, and the elves call her wise. Her teacher found out how and taught her, which she says after Arya asker her how she did it:

I used a trick ... I Learned from my master ... Tenga ... ages ago. May a thousand spiders bite his ears and knobbly bits.