There is a good possibility that he has gingivitis - - that would account
for the bad breath.  If there is actual puss, he needs a vet, stat.  Those
teeth have gone beyond the state of "merely bad".  Can you lure him with
something yummy, like sardines?  Best to have a partner, and a cat carrier.
Let him have the spoils of the catch once he is in the carrier.

It is always best to use 2 people when dealing with wiggly kitties.  And I
agree about the suggestion to have him neutered.  Might as well have that
done while the teeth come out, because it sounds as though they might be bad
enough to do so.

Another thing that can make feline breath bad are high levels of urea in the
blood (kidney failure).  Your vet will know best.

Best of luck with that puddycat!

Mel