Well, I know this seems to be something a lot of people neglect, but status effects and stat boosting moves are very good, and can solve that problem for you unless you're dealing with something so dramatically above your level that you can't survive a single hit. Even then, those items you never use that boost stats in combat, such as X Def, are actually surprisingly helpful for such things, especially if you can get off a move that lowers your opponent's accuracy so you can set up. Something as basic as using Sand Attack twice can be crippling, as it lets you set up on things that can 2HKO you. Then you can Dragon Dance up and sweep the other team, even if they outlevel you. Also remember that the enemy trainers frequently carry full restores, so a move such as Leech Seed that doesn't count as a "real" status effect is far preferable to Toxic that they'll just cure. Obviously, using them both is even better still, but if you have to choose, go with the one they can't get rid of, as the CPU basically never switches out.
Being outleveled definitely makes it harder to just choose super effective moves and OHKO without issue, but it doesn't prevent you from disrupting the opponent in any way unless their stuff is both faster than you and capable of OHKOing your entire team, which only 10 levels of difference isn't going to do. You have to get upwards of 30 levels of difference before they can threaten that.