2002 pt cruiser was running fine shut down on highway let out smoke and oil on motor wont start

Sounds like a bad turbo to me. When you "kick it in", the engine falters and you get black smoke for a while. What is probably happening is that the turbo is leaking oil into the intake air stream, putting it into the cylinders with the fuel/air mix and causing one of two issues. Either the oil is inhibiting the combustion process, causing the falter and the resulting poor ignition, plus the oil, is giving black smoke, OR, the oil in the cylinders is fouling the plug momentarily, resulting in the fuel/oil being passed into the exhaust stream, burned in the catalytic converter and exits as black smoke. If it runs OK except when under turbo load, have that thing checked out ASAP. And, as far as the light staying on, most faults will set permanently after they occur three or more times within a certain period of time. This is ti ensure that intermittent faults won't cause false setting of the light.

sounds like an air pocket in your cooling system need to bleed system and add missing coolant

Did they do a charging system check, check starter and alternator first more details plz and i may be more help.

Your engine oil light is a problem. You may have run out of oil and if the engine is run with too low of an oil level it can seize up. You may need to have that engine replaced. This is why it is important to check the oil regularly and to have it changed per manufacturer's recommendations.

run the fault codes
indicates a problem crank or cam position sensor

Don't try start the engine when the oil light turn on, it would harm your piston, camshaft and crankshaft
It should be the oil pump has broken and need to replace, tow your car to the nearest service center

You can take it to auto zone or advanced auto parts house and they will check the codes for you for free.then you can look up the code on internet and see whats going on hope this helps

This sounds like a transmission issue, did you get any error codes?

Is the check engine light on? Try spraying carb. cleaner in FI. and start. If it starts and runs until fluid is dry, might be fuel pump. If engine light on and has been for awhile, could be cat. converter stopped up and engine can't breathe so it shuts it off.

you might have some wire toughing the ground rabbing when put it in reverse the eng shiftting causing wires to stretch and might touching ground or hot wire