Superfast1

At that age & mileage, I wouldn't be surprised if you're experiencing a failing torque converter lockup which causes the transmission to slip in & out of gear. This condition matched your description when you mentioned you can hear the engine revving when you step on the gas but the car doesn't move for a second then lurches. However, this condition normally happened when the transmission is cold. Nevertheless, you should check the condition of your transmission fluid. If it's clean, it's translucent, in deep red color & doesn't smell burnt. You also need to check the fluid level after the car is warmed up, idle in park & on a level ground. The next step is to have a transmission specialist to take a look. If it's indeed the transmission, then I highly recommend a transmission overhaul instead of getting a used one as you'll end up with the same problem down the road.

CLLEXUSS

There are some things that require advanced diagnosis. That's the problem you are encountering, you don't have proper diagnostics. I don't like the fact that it's not getting fuel economy that it should. You are indicating it's not your 02 sensors, generally running rich that's the first thing I think of but there can be many other reasons. It just depends how much time you have to try and figure this out. If its your daily driver I'd want to figure it out sooner, if you have time and the car doesn't get used that much then you have time. But if you need to use it a lot I might look for a shop that specializes in Toyota electrical that can diagnosis this properly, you don't have the right testing equipment that you need. It's going to cost to run the tests, but it might cost more down the road if you keep driving it this way. You really need to find the right shop though. You don't have to pay them to fix it but if you can give them a couple hundred bucks for their time and diagnostic tools, then you can do the rest and make the proper repairs.