This very type of question was discussed here:
http://www.themanadrain.com/index.php?topic=39821.0My recent standard play has brought up a question, for which I've been given a contradictory answer to.
This card's activated ability is worded like Mind's Desire with regards to playing the card that is revealed, more or less. I had asked a judge and was told that I could play a land that is revealed with the Djinn even if I had already played one for the turn and don't have another card that would allow me to play more than one land a turn. I followed up the question with, "does me playing the revealed card have to be a legal play? For instance can I play a creature, enchantment, sorcery, etc on my opponent's turn with the Djinn?" I was told yes that I could.
If you reveal a land with Djinn of Wishes and have already played a land this turn, you are not able to play the revealed land unless you have some other effect which allows you to play an additional land, and can never play a land when it is not your turn.
Djinn of Wishes' and Mind's Desire's wordings are not the same. Djinn of Wishes reads, "You may play that card without paying its mana cost." Mind's Desire reads, "Until end of turn, you may play that card without paying its mana cost." The Djinn is telling you to play the card right now, so you must play it during the resolution of the activated ability (or not at all). Mind's Desire gives you a duration on when you can play it (until end of turn). So with the Djinn, you can cast a sorcery, enchantment, creature, etc. even if it's not your main phase, since it ignores timing restrictions. (It's during the resolution of an activated ability, not a time when you could normally cast any spell, even an instant.) Mind's Desire is not telling you to play the card right then, it's setting up a duration within which the card can be played, so any timing restrictions must still be obeyed.
For Three Wishes:
Basically with the removed cards. It say you may play them until your next upkeep.
So that would be no, you couldn't play the artifact outside of your main phases.