Here is a summary of all of Loki's exploits in his continuity. There have been major changes in the more recent past, as Loki attempts to shift his story onto another track. Though his canon goes back literal decades of comic history, Loki is now attempting to reinvent himself since his death, so the bits starting with "Trickster Reborn" are the most relevant. His past self continues to shape him, though, and is a constant tension he has to deal with.

This page is a specific summary of his 'Kid Loki' incarnation, who is technically now dead and gone, taken over by the spirit of old Loki. But Loki has stepped into that role, and appears to have a desire to change, as the young Loki did. Whether or not he actually can is an open question.

The historical Loki is a trickster god with the ability to literally shape space and time through magic. He is shown to travel back in time at a whim and change history, creating new stories and myths and laying the groundwork for his plans in the present and future. Magic is the art of telling a story so vividly that it becomes the truth, and so any story he can convince the world of, becomes the truth.

However, it seems that his current incarnation is choosing to be more constrained. In fact, he has stated that he doesn't want to use his magic much, because the more he uses it, the more that the power of legend dictates who he is. The old Loki became trapped by his use of magic, becoming not just the god of mischief, but the god of evil, because of the strong effect that story has on gods. This new, reborn Loki wants to change his fate - though it seems that he's destined to fail.

He's also stated that his younger, smaller body constrains his abilities. He doesn't have the strength yet to do as much as he once could.

As such, Loki relies far more on his innate more mundane abilities and various toys, than on pure world-warping sorcery. However, he does use his abilities to cast spells, such as teleporting around, affecting spells cast by Billy Kaplan, and casting glamours and illusions. His ability to do magic literally is unlimited except by his imagination and his power level.

Other than that...

He can shapeshift into anything - so long as it's Loki. (At one point, he tells Lorelei that he can't turn into a fly, because he's not a 'tiny fly' kind of person, but he can and does become a woman and a fox, just to show off. He's canonly turned into a magpie as well). Of course, using illusion magic he can look like anything he wants, but it's an illusion.

When it comes to equipment, he has a pair of seven-league boots that he can use to climb buildings or walk on tightropes. He has a coat that turns him invisible, a medallion of invisibility AND a 'belt of science' that can turn him invisible - he can be really, really, really invisible. He also carries his ancestral sword, which he seems to be able to pull from thin air.

He has excellent sleight of hands abilities as well. You know. Because he can.

I don't really know if this qualifies as a separate ability, either, but he also appears to be able to create and enforce magically-binding contracts, just like the devil. He switched a contract that Mephisto was trying to make, for a differently-worded one, and sealed it in blood, and it did work. I suspect that he wasn't just tricking Mephisto and piggybacking on his abilities here, since, yanno, Loki is also Satan and used to rule hell. So I'm going to say that he does have this ability in and of himself.

TBH who knows what else he can do. Probably a lot of things.

Oh yeah, and he's a world-class hacker. And he writes slash fanfiction on the internets.