People say 'what the hell!' in the UK. I can't recollect hearing 'what the heck!' on too many occasions. That expression is more American than British. 'Drat' is extremely old fashioned. I wouldn't use it.

"Drat!" is just a mild way of expressing annoyance or anger. Let's say the mild version of "F##k!"

"Drat" sounds very old fashioned - I have never heard it used in British English. "What the heck" is very much an American expression, probably a euphemism for "What the hell". Again, although you will hear British English speakers say "what the heck" occasionally, it is much more common for younger people in particular to use much stronger expletives these days.