I've killed hundreds of these things in FO3 and FNV and I have no idea where they came from.

They are a pre-war living bio weapon based on Jackon's Chameleon. Or perhaps rather, pre-apocalypse. US Army was planning on dropping them to China during the war, but never got the chance.

http://fallout.wikia.com/wiki/Deathclaw

Mutated from eating too much fast food.

Exactly that but they seem to gloss over the fact they also managed to concentrate pure evil in liquid form and injected that, then poked them in there privates with a sharp stick to get them pissed. Add 200 years of natural rad selection and them harboring a grudge and bingo.

Lovely and cute ,

A must have pet,

great for children

IF you dont like your children

I don't think it's been fully confirmed what or how they were made, got to the part in Fallout 2 where someone guesses they came from the Jackson Chameleon but he says they have many things in common but more not so it's a bit werid.

It's also strange how they've expanded all over the US in areas some distance from any labs...

Play Fallout 1 and 2 and you will know

ToJka is correct, the deathclaws mutated from chameleons, and yes I can also confirm what he states that they were actually developed as a military weapon.