In Warhammer 40k is it possible to have your army use vehicles from other factions?
Yes and no  

In the current edition, all armies (except unbound armies) are made up of formations.  For example, you might take the Combined Arms Detachment from the basic rules, or any other formation from your codex.  Which army you are using is basically determined by which faction your warlord is from.  You can take formations from other armies and books, however, as long as you follow the rules for allies, located in the rule book.  (I don't have my book with me to get a page reference).

So, you could take a Harlequin Combined Arms Detachment and also take an Eldar Warhost, which would give you the ability to take a lot of Eldar stuff, as long as you fulfill the requirements of the formation.  I'm sure there are other Eldar formations that would have less stringent requirements, as well.

Additionally, you could take an unbound army, which has no force org requirements, but also grants none of the special rules associated with formations (no objective secured or warlord trait reroll, for example).  In that case, you can take exactly whatever models you want.  You would still have to follow the rules for allies, though, which can make movement or deployment difficult if you pick armies that do not like each other.