The words Rompicoglioni, Stronza and Troia may be difficult to find in certain translation dictionaries because of their vulgar and offensive meaning. They are three good examples of Italian parolacce or swear-words, so readers of a sensitive disposition need not read on!
This term is actually made up of two words; rompere meaning to break, and coglioni referring to the male genitalia, specifically the testicles. Rompicoglioni can literally be translated to 'ball-breaker' and refers to someone of an irritating or fastidious nature.
Although this expression would be less than common as a literal translation, its closest equivalent 'pain in the ass' is deployed fairly frequently as an English expletive.
An entry for the word stronza (or it's more common masculine counterpart stronzo) can be found described as a 'solid excrement of cylindrical form' in one leading Italian dictionary, and is the Italian form of the word 'turd' in English. Stronzo can be rather versatile and is used in more that one context, the most common of which is as a noun; strongly denoting someone as being either extremely stupid or insensitive. The English equivalent based on this context is more closely mirrored by the word 'asshole' in English.
Is actually a harmless zoological term used for a female pig that is singled out for reproducing, but the offensive connotations based on this meaning are pretty obvious... Its more straightforward use is to negatively label a woman who is sexually active with a large number of partners (i.e. Slut in English), but it can also be used to convey any number of negative attributes, much in the same way that the word 'Bitch' is used in English, with 'che troia!' being a popularly used expression meaning 'what a bitch!'.
Remember that all three terms mentioned above are vulgar and inappropriate in normal conversation, and can often be replaced by less offensive terminology. If you're planning a trip to Italy any time soon, I'd recommend being careful how liberally you employ these words.