Actually, a twat might be a vagina, but the term is more often used to describe a person than a body part. A female person. The male equivilant would be a prat.
It's more insulting. It's like calling a man a cunt. Or, more precisely, saying he's as dumb as a dumb woman. Calling someone that in a pub is a quick way to leave without paying your tab.
nowhere near as offensive - that's pretty much the last bastion of offensivness. the most offensive word in the language even.
twat isn't too bad. more of a "silly" than a "stupid". a somewhat jocular word, although tempered by the adjective you pair it with. generally an aspersion on inteligence - but mostly used in the context of friendly banter.
it has added potency in the rare case it's used referring to strangers, but again there's worse expletives.
"you were so drunk you couldn't even see the minger you pulled last night, you twat!"
"the barman shortchanged me, the stupid twat!"
"you look like a right twat with that shirt on"
"i was chatting this bird up until that twat came over and shat all over me" (while pointing at a friend)
"who's the twat in the suit?" (referring to a boorish lout introduced into the group as a friend of a friend)