Engine misfiring and jerking?

My wife's 1996 Corrolla brokedown recently and had it towed to the mechanic. Turned out that the distributor needed to be replaced along with a new set of plugs and wires. However ever since it has been replaced, the car seems to misfire intermittently. It happens more at higher speeds above 55 and when going uphill but not always. I recently noticed that at higher speeds if I quickly press and release the accelerator repeatedly I can get it to misfire. I took it back to the mechanic and he can't replicate the problem (ofcourse)! Please help!

This is "the winter beater" and has been a no service problem vehicle for years. In the past few months, I have noticed making right turns that I get a hesitation in the accelerator. It also shows up when the gas tanks nears E while driving on the open road. My assumption was there was perhaps water in the gas tank.

About 2 months ago, I suddenly found that if the car was sitting for a few days, it would crank but would not fire. Cranking for 2-3 minutes would finally bring a fire. Then another. And another until it was continuous to start the engine. That soon dropped to the car sitting for a day and it would not crank properly. If the vehicle was in the cold, no fire at all even after cranking for 10-15 minutes. If it sits in the hot sun, it cranks and fires right up.

What is so amazing is once the vehicle starts, it runs like a charm with no problems at all.

About three weeks ago, the check engine light came on. I still had the problem starting it and thought maybe a fuel pump was going bad. Then suddenly, I was driving and had "dead air" on the gas pedal. It would go 2 mph in a foot off the pedal state but any attempt to use the gas pedal yielded nothing. It stopped on the highway. I cranked it, it started right up, then drove fine.

I took it to a local fix it guy. He says the diagnostic is pulling multiple, multiple misfires. He is finding oil in the distributor but did not pull it as the screws will sheer off if he does. He is saying with the shaft set up and all the sensors, it is beyond the scope of what they do.

Prognosis? He says run to dealer and let them "play with it" to see what will fix it.

Any ideas here what to do? I'm already resigned to tune up, points, plugs, etc. But what is truly going to clear this distributor problem? How does oil get in there?

My car runs well but frequently in the morning when I switch it on, It idles Ok but when I press the accelerator to revv it idles poorly, vibrates and almost stalls untill I ease off the accelerator. When I alsopush the accelerator harder above 2500RPM it behaves ok. Less than that it wants to stall. After driving for a while 10 min, it is fine No problems while driving.
I have had Air Filter, Oil Filter, Plugs and Spark Plug wires relaced recently but problem persists.

What could be the problem?

Thanks 2CarPro Jack for giving me some clues to investigate further.

I had a chance to observe it this morning. I switched it on and it stalled. I switched it on again and it started OK and maintained idling. I went under the hood and revved a little. It behaved the same as described in the earlier post. After a few revving for two minutes the the vibrating (and the wanting to stall) during revving was gone.
No visible smoke is observed from the exhaust.
I'm using the original Denso Spark plugs K16R-U11
It once set the check engine code on the Throttle Position sensor but the mechanic 'reset the cars computer' That's what he said. Nothing since then.

After that was done car acts like it not getting gas to it, done a test reading to it the reading codes came up P300, P302 & P303 which states random misfire on cyclinder 1, 2 & 3 my problems is when I step on the the gas pedal it doesn't want to go it

Also now my check engine light is coming on.

Other Category problem
1996 Toyota Corolla 4 cyl Wheel Drive Type unknown Automatic 96.000 miles

when I step on the gas pedle it runs a little rough, then when I take my foot off the car jerks back and slows down without me stepping on the brakes. Thought it would be the fuel filter. What could it be?

Car engine misfire and it****** like if it was sucking too much air