The fact that you add oil to the fuel in 2-cycle engines changes many of the fuel's characteristics, including the ways in which it rots and the cleaning procedures required to remove it. Whereas most techniques used to refresh a 2-cycle's fuel system are almost identical to those used for conventional 4-stroke applications, care needs to be taken to rid the system of spoiled oil as well as fuel.
Old 2-cycle oil has two basic problems. The first is that the oil itself becomes unstable in the presence of solvents like gasoline, thinning it and converting its inherent viscosity into a sticky film that clogs filters and carburettors. This varnish is similar to that found in any gasoline engine, but the disassembled oil molecules make it thicker and stickier.
The second problem is that most modern gasoline contains ethanol, which can eat fuel lines and hasten the breakdown of oil. Along with the usual fuel varnish, dissolved rubber works its way though the system's filters and into the carburettor's small passages.
If your engine has already been run with bad fuel but still works, you might be able to get away with a 2-cycle-specific marine fuel conditioner like those sold by Evinrude. For an average of about £3 a bottle, as of 2010, such fuel conditioners do a great job of dissolving built-up varnish and gum in the fuel system. You could use a standard automotive additive, but many of these do such a good job of dissolving oil that they break down the molecules required to keep the engine slick and happy.
Marine additives are used like any other; simply add them to the tank (227gr. of additive for every 32 gallons or less of fuel) and run the engine at part throttle until the tank runs dry. If the engine still runs badly, then you'll need to go a little more in-depth with your cleaning.
If the rubber molecules floating around in your fuel system have irrevocably clogged the fuel filters, replacement is necessary. After you replace the in-tank fuel filter, the inline filter and the carburettor filter, you should seriously consider replacing your stock rubber lines with those specifically designed for use with ethanol. Otherwise, you're looking at perhaps two years between line replacements.
Really gummed up fuel systems will require disassembly and cleaning of the engine's carburettor or fuel injectors. With the carburettor apart, you'll want to focus your cleaning efforts on the needle valves and jets, as they're the fuel system's natural choke points. You can soak your valves and jets in liquid carburettor cleaner overnight, but replacement may be simpler and more reliable.
Fuel injectors are expensive, so cleaning them should definitely be a priority. The procedure is a bit complex and requires a 12-volt power source that can be repeatedly cycled on and off, but such setups can be built at home. If you lack the materials or confidence to build a simple injector cycler, then you can get 90 per cent of the way to perfectly clean injectors by simply suspending their metal bodies in liquid carburettor cleaner for 24 to 48 hours.