...
So,
1) If they hacked into my machine and stole the private key; (illegal)
2) If they sniped the pk while snooping on a public access connection; (illegal)
3) If they brute forced the private key into existence; (not illegal)
4) If they snapped a shot of my private key qr code over my shoulder at an ATM. (not illegal)
What if I claimed an address on the block chain with a signature and 3 or 4 happened? Would I have a case then?
Pretty much correct. I have my doubts whether 4 couldn't be classed as illegal though. Most of definitions of 'hacking' in criminal law describe 'anauthorised access' and that could fall under that definition (similar to stealing your credit card details).
But in any case, if you know the person who got your bitcoins, you could try to get it back by starting civil lawsuit against that person.