How to get realistic Skinless and Screamer mutants?

Well going by the crazy scientist experiments on humans makes this much "simpler" than radiation (understand we'll naturally need some handwavium for it to work).

Beginning with the screamers, as they seem a little more plausible and easier to explain:first things first, they'll most likely have a more and thicker hairs as well as more melanin in their tissues. These measures would make cells more resistant to UV radiation as well as offering some level of protection against the cold. The ability to hibernate would be a great way of dealing with lack of food, as the creature can take refuge and sleep for a certain period until the environment becomes more favorable. This strategy is already used by many animals to survive during the winter as well as by fat tailed dwarf lemurs to survive the dry season. Fat reserves are also a great way to both protect against the cold as well as serving as necessary energy storages. These protections against cold however might make it so they deal with heat a bit more poorly. The only way I'd see them being more capable of dealing with heat would be the ability to get rid of their dense fur when required.

Essentially, your screamer would be relatively similar to a genetically modified mountain gorilla, a powerful primate which is already strongera and more resistant to the cold than humans, is intelligent enough to use tools and learn sign language. It can't be simultaneously resistant to large amounts of heat and cold as far as I'm aware, sadly, but with proper mechanisms, it might be able to adapt to both, similar to how some mammals change their fur between seasons. Regarding radiation resistance, I'd go for the tardigrade protein shielding, which basically protects their DNA without disrupting its functions.

Now, the skinless. This is a hard one simply because it can't be literally a species of undead animals unless you're willing to accept magical ghouls. So in here we need something that lookslike it's decaying when it's actually not.

The first part (missing eyes, noses, ears, etc) can actually be explained without much trouble: these creatures are very aggressive even to one another, and their immune system is very efficient, ensuring that they can survive such attacks, which are usually directed at their faces and some other parts of the body. These wounds however make them neutrally less effective at hiding and hunting, and thus they might be the ones seen the most simply because they are growing desperate as they can't quite capture their usually prey as well and humans look edible enough, especially when you're starving. This trait of the most sighted skinless being the ones sporting greater wounds and who have been less successful at eating would Allow potentially explain them being relatively skinnier than their well fed counterparts, being a side effect of lack of proper nutrition and further stimulating aggressiveness in them specifically.

Now: the rotten quality. My best guess to make them more or less smell like a dead body and to look like they have fleshy rotten chunks of skin dangling would be to would 1-make them mostly carnivorous and decently intelligent, as well as strong, and 2-make them ambush predators. By giving them relatively tough skin and a good immune system, we could have these creatures going through the following strategy:

1- they capture prey and eat the bits that interest them, leaving predominantly the skin and ottheir bits relatively untouched.

2- they wrap some of these bits (especially the skin) around their bodies, giving them a smell of rotten meat and making them look a bit more like a decomposing corpse.

3-lay down near scavenging "hot-spots" (closer to the scavenger's usual territory and scavenging grounds) in the open with other uneaten chunks of dead prey, waiting for a scavenging animal to explore.

4- swiftly attacking the scavenger once they're close enough, snapping their necks or choking them to death with their surprising strength.

5- eat their fill and repeat.

This strategy, assuming they can withstand the bacteria that will grow in the chunks of dead meat wrapped around them, would not only allow them to exploit the scavengers as a food source, it would make them more and more similar to a corpse, with the several dirty and rotting chunks of skin around them becoming harder to distinguish from their own tough skin. It'd also make it easier to mistake them for actual zombies as a human That approached a supposed corpse only to be attacked by it clearly wouldn't try to check clearly whether the worn out chunks of rotting skin did or not belong to the "zombie" or to another animal. Regarding their own creation: perhaps a subspecies of screamers, made by the same scientists to be more well adapted for warmer and drier environments, with grayish thick skin and a slightly slimmer build helping to conceal their actual strength superior to a human's.

As with most modern zombie franchises, the answer is ultimately illness

Radiation doesn't mutate the way Hollywood and the golden years of science fiction would suggest. But science has figured out what it can do: it can compromise the immune system.

The cells of the immune system are among the most highly radiosensitive cells in the body.

There are necrotizing skin infections that, combined with whatever disease creates the zombie-esque creatures you're looking for, would result in the skinless creature you want. Radiation compromises the immune system, necrotizing cellulitis sets in, and the disease mutates to become chronic and resistant to available treatments in your post-apocalyptic world.

Your screamers, on the other hand, are a bit of a problem. Radiation and disease kinda always lead to weakness, not strength. So in this regard I'm going to refer to the original story line from the game Fallout where the supermutants were compromised forms of super-soldier research (the Brotherhood, if I recall. Correct me if I'm wrong). So, if we had Captain America immunocompromised by radiation and then subjected to some form of illness that turned him into a zombie, you'd get your screamers. Especially if the illness somehow leverages chemistry to produce berserker/blind-rage disorder. (One theory, lacking sufficient evidence, is that it can result from Paget's disease, which leads to uncontrolled skull bone growth that puts pressure on the brain. May not be a direct link, but it meets the suspension-of-disbelief standard.)

Note: You didn't mention the berserker aspect of your screamers , but I jumped to a conclusion. Kinda smells like DOOM or Resident Evil to me. Am I wrong?

Ultimately, the real problem is once you have your disease-riddled creatures, how do you keep them alive. I leave that one as an exercise for the reader as it often requires some kind of hand waving.

Screamers could be the result of a project by ethically dubious genomists, freed from oversight/regulations, trying to "improve" humans, then losing control of the project. The "improved" humans would naturally be better-adapted, with the traits you mentioned engineered in, and would thus survive.

Skinless is trickier, as the traits you mentioned would seem to impede survival and reproduction. Perhaps they're exiles from the human colonies, who were thus exposed to more environmental hazards/radiation, and thus appear horribly diseased etc? Though as a caveat to that, they would be short-lived, and wouldn't likely be able to sustain a lineage, and their presence would thus depend on a certain rate-of-exile from the human colonies.

the skinless are people who survived the radiation and lived out side for generations, but became inbred, only small populations suried, as such they are insane and prone to leprosy. This is only increased and worsened by the radiation. so it is a mix of incest and radiation.

The only one I could think of is the skinless which could just have all those features burned off from the nukes.