I found a stronghold in my world and I just can't find the end portal. I have been looking forever and I can't find it. Is it possible that there is no end portal in this world?
It's possible but unlikely. End Portals do spawn in strongholds in the console version of Minecraft, so it's not an issue of version. It's possible, however, that the portal was overwritten by something else in world generation (a dungeon in precisely the same place, or a mineshaft running through your stronghold).
What is more likely, though, is you haven't searched the entire thing. Strongholds are quite extensive, so it can take a long time to go through the whole thing (speaking from experience, I have made bases in strongholds a few times. They can be huge).
Unfortunately, since you are on the console version, ender eyes only point you to the stronghold itself, not the portal, so the only real advice I can give you is to keep looking, and clearly mark where you have been. I like to put torches on the right-hand side of corridors as I move through them, so I know if I am backtracking or not.
If you're running low, on ender pearls, go to a desert that isn't highly lighted, try to not place to many torches if possible, get to level 30, and get a Sword with Looting I or higher, then the enderman, WILL drop something, and throw them, to find the stronghold, and look through the entire thing, that should about do it....