My suggestion is to research actual mutations that have been documented in that species or related species. The kinds of mutations you tend to get after radiation exposure are frequently things that could've happened anyway, but radiation made it more likely. And then you rule out the ones that would be completely non-functional and get weeded out immediately, and put several of the better mutations together to create a new creature.
Now, let's take a look at the ideas you came up with
Rad-Rats - those seem reasonable. Plenty of natural mutations in many species result in a creature that's larger or smaller than normal. Get several size-increasing mutations in the same population, and have some kind of selection pressure for getting bigger, and you'll get bigger rats pretty easily. And since there already are rodents of similar size to your Rad-Rats, you know there's no major functional issues with having a rodent that big.
Trihorners - those are a bit more of a stretch than Rad-Rats, but still fairly believable. I'd probably draw inspiration from komodo dragons, as they're a fairly large terrestrial apex predator lizard in real life.
Giant Scorpions - these are not so realistic. There are two big problems that have kept terrestrial arthropods from getting that big. 429
Firstly, the way they breathe is fairly inefficient at larger sizes. Even animals such as tarantulas and such are starting to hit that limit, and have limitations on their activity that smaller arthropods don't have because they run out of breath. The second problem is molting. In order to get bigger, an arthropod has to shed their exoskeleton and grow a new one periodically, but while they're growing the new one, they don't have as much support on their body. If they're too big, molting will cause them to collapse under their own weight.
Skinless - these also don't seem very realistic to me. The closest real-life analogue I can think of are people who are prenatally exposed to chickenpox, but they are missing patches of skin, not all of it. Skin is a vital organ, and people who are missing too much skin tend to die without intensive medical care. I also don't get why they're insane and violent. In real life, looking freaky and acting scary aren't really linked at all, especially if the person's looks aren't a choice. 671