Idle ok,slow acceleration fine,accelerating quickly miss-fires

Check your vacuum line for the cruise module under the hood.

Some general thoughts - -
when you try to accelerate, a couple of things happen. The engine shifts sometimes, and you put it under a load unlike when it is idling.
Is it possible a wiring harness or a hose is moving when you accelerate ? Is it possible the fuel pressure or ignition module is not good enough to handle the engine under load ? Is the EGR opening early or something causing a vac leak and a lean fuel mixture ?

Check the battery cables. I had the same issues with my 96 tacoma, The battery cable connection at the battery can be cranked down but still be loose. Hard to explain, doesn't make sense, but just check it out.

Ok. I'll give you my best guess, although I am not a Dodge Stratus expert. Based upon your description of the problem, I am to assume that the vehicle has problems accelerating up to speed, but once there, cruises ok unless you are going uphill or need to accelerate quickly, then power falls off rapidly and acceleration returns very slowly. If that is accurate, I would suspect the EGR valve. This is because at ihighway cruising speeds the EGR valve is pretty much wide open, letting exhaust gases back into the intake. When you need to accelerate, pressing the accelerator results in intake vacuum drop. This is partially compensated for by closing the EGR valve. If the EGR fails to close or sticks partway open, the exhaust gases will lower intake vacuum even further, and rob engine power. This can also cause the onboard computer to force a downshift to the transmission, as vacuum sensors are used to determine engine loading and the need to reduce gearing. In addition, a partially open EGR valve can cause erratic idle as it affects static intake vacuum (EGR is normally closed at idle) and the onboard computer must continually compensate, resulting is unstable idling.

most misses are injector related either from dirty injectors , low fuel pressure ow injector wiring faults
use a quality injector cleaner for a tank or two
run the fault codes to check for other related sensor problems

Even tho the ignition seems ok, I'd check the ignition cables to the plugs. Sometimes these break down over time... it will idle and drive ok, but when you need power for a hill, or acceration, that's when the wires faults start to show up.
A quick test is to put the car in drive with your left foot on the brake FIRMLY while you press the accerator... if the miss and lack of power shows up, it's usually the ignition cables to the plugs.
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check transmission fluid.change fuel filter and air filter.try changing up on where you buy gas .because bad gas causes problems.

the idle controls could be the problem

I had a power problem, when cold idled just fine,when warm it would miss at idle, spudder on acceleration and sound just fine at higher rpm. found number three spark plug wire had burned through lower boot. Spark was firing to head at low idle. same wire burn twice with about 40000 mile between.