Mass Effect has always been a rather odd leveling experience. You can’t hit the max level of 60 in a single playthrough, even if you do all of the content. Obviously, if you’re looking for ways to level up quickly, then complete all of the side quests and mining opportunities on every planet. Don’t use any Medi-Gel because when stocks are full, you get 450 XP for each one you pick up. Opening crates, unlocking doors, finding Codex information and talking to every character is also key for either earning XP or opening up future opportunities for earning more.
Another useful strategy for Mako missions is not to outright kill enemies with the vehicle. Instead, use it to bring their health down and then get out and finish them on foot. This provides even more XP than vehicle kills do. You can also earn additional XP when exiting the elevator in the Citadel and killing multiple Geth Destroyers during the finale mission; killing additional rocket drones in Bring Down the Sky (in the second torch station’s top floor) if one to two enemies are still alive; and killing additional waves of Geth on Casbin for the mission UNC: Geth Incursions (make sure you don’t destroy the Geth Dropship).
Of course, there’s also the new Legendary Mode introduced in Mass Effect: Legendary Edition, which scales the level cap down to 30 for Mass Effect 1. The amount of XP earned throughout the game is still the same though. If you’re keen on streamlining the overall leveling experience and don’t care for more incremental power upgrades, this might be worth opting for.
For Mass Effect 2, you’ll need to import a character from Mass Effect 1 and do a second playthrough. The latter provides bonuses for XP so even though you won’t have retain the same level as your first playthrough, it will still be easier to hit the level cap in the second. Again, do every side mission, main mission and assignment to gain XP while killing every foe that you come across in combat.
In Mass Effect 3, you’ll have to import a character from Mass Effect 2 and, once again, don’t use any Medi-Gel. Any surplus Medi-Gel found will thus convert to bonus XP (which increases based on the difficulty). Play through all of the DLC as well as the main missions and side missions. If you’re still having trouble hitting max level, play through on New Game+ for the XP bonuses.