Why does my Neon have a loss of power when attempting to accelerate?

When the Check Engine light is on, a diagnostic fault code has been stored in memory. Start by reading that code. It will get you into the circuit or system that needs further diagnosis. Chrysler makes that real easy. Cycle the ignition switch from "off" to "run" three times within five seconds without cranking the engine. Wait a few seconds, then count the flashes of the Check Engine light. You'll see a series of flashes, a short pause, then another series of flashes, then a longer pause. Those are the two numbers of the two-digit code. Additional codes will flash the same way. The last one will be code 55 which can be disregarded. Holler back with those codes.

I'm confused because the misfire detection came about in the '96 models with on-board-diagnostics, version 2, (OBD2). I don't recall ever seeing a misfire code on a '95 or older model.

With so many codes showing up, I'd suspect they all have a common cause, typically a common ground or feed wire, but the oxygen sensor and the purge solenoid don't share anything. You might want to look at the electrical connectors for signs of corroded pins or wires hanging down on hot exhaust parts. Corrosion can create a current path between multiple terminals and multiple circuits. That will cause more trouble in humid or rainy conditions.

The next thing to do would be to connect a scanner that can display live sensor data during a test drive. Of particular interest would be the MAP sensor, based on your description of the symptom. As long as the voltage from that sensor remains within 0.5 and 4.5 volts, it won't set a fault code even though that voltage could be wrong. That sensor has the biggest say in how much fuel enters the engine. When it starts to fail it can cause stumbling or a hesitation. When it fails completely, the engine will usually still run, but very poorly, as long as the gas pedal is moving. The engine will die as soon as you hold the pedal steady. Check the vacuum hose going to that sensor for leaks too. That will cause low vacuum which normally occurs during acceleration, so the Engine Computer will command more fuel than needed. That will result in black smoke from the tail pipe along with poor performance.