How is it that a computer receiving packets through wifi doesn't get those wifi packets distorted often?
It does.
Wouldn't things like other radio waves interfere with the signal often?
They do.
How does my computers NIC deal with that?
Error correction, equalizing, flexible synchronization, re-requesting lost packets on different layers.
Like what if the website data being sent from my router had the signal distorted through like radioactivity if I happened to be in Chernobyl...
What?! Radioactivity falls into different categories, but none of them interfere with RF signals. If you put your router on top of something that emits a lot of ionizing radiation, then the computer chips inside will malfunction. But that has nothing to do with RF.
The knowledge I have regarding how wifi works is that interpretation of the data is done through looking at the amplitude in the waves and the frequency and sin etc.
You don't seem to posess a lot of that knowledge, to be completely honest.