If they keep adding refrigerant and it blows cold for a while, and then starts blowing warm then you definitely have a leak! I could refer you to techinfo.toyota.com where for a $15 subscription you can have a "2 day pass" to every repair manual, wiring diagram, TSB, etc for your vehicle. This may be useful for a different concern, however A/C concerns are best left to professionals as it is illegal in most (if not all) states to handle refrigerant without the proper license/certifications. For A/C work and diagnosis, you really need to have the correct tools and experience to service the system... in which cases would cost you more than paying a professional to fix it correctly.
If you've taken it to several different independent shops with no results, i would have to really recommend you take it to a Toyota dealership. The techs at the dealership are experienced with toyota's in particular. The independent shops are kind of like your "family doctor". adequate for many things, but if you need something that is out of their area of expertise they refer you to a specialist, in this case the Toyota dealer would be the specialist. They will likely be a little more expensive than the independent shops, but are far more likely to actually fix it right the first time, instead of taking it to 4 of 5 different people who all do the same basic thing, and end up with the same basic results.
Here is what you can expect the dealership to do. First they will check pressures with a set of gauges, and then likely vac and charge your system with fluorescent dye. If your system is leaking as quickly as it sounds like it is, a qualified mechanic should be able to identify the source of the leak that same day by using a UV light and special glasses that make the dye glow, pinpointing the source of the leak. However if it is already full of refrigerant and there is something else wrong with the system, this can be identified by checking the pressures with a set of gauges. One way or the other, within 5 minutes they will know which direction they are going... leak or failed component.
Expansion valves sticking are relatively common in that year range. The valve itself is around $50, and i'd figure about 3-4 hours labor to replace it.
IF it is leaking, then it could be as simple as an O ring (about a dollar) plus labor to vac/charge the system, or it could be a condenser or evaporator, either of which is capable of leaking. Leaks in the lines themselves is very rare, they usually occur in the evap, condenser, or an O ring at the compressor.
I hope this helps give you a direction, and general process of how they will diagnose your concern. but if you have any specific questions please feel free!