Your OSCar is working perfectly, everything is responding smoothly, except that it wouldn't keep the presets in memory after switching it off.
This is the usual symptom of an exhausted internal battery. Almost every old synth (as long as it has presets) will probably need a battery to store them into memory. After many years of operation, batteries lose their capacity and therefore internal memory gets lost.
This is what you need to do to replace the battery on an OSCar:
1) Remove the 6 screws on the rubber sides and remove the front panel. Keep an eye on the small "discs" on top of the knobs, they tend to fly everywhere...The battery is located in the middle of the circuit board (see that white round thing?)
2) Desolder te old battery. It should have 3 pins, like in this picture from behind.
3) Get a replacement battery. I was lucky to find a perfect one, with the same pins, sligthly different shape, but it fitted perfectly (sorry, I don't have the exact part number anymore...)
4) Fit the new battery, solder it in place. You will have to put the old preset data into memory using sounds from the original cassette, or a MIDI sysex file.
Try this MIDI Sysex File for OSCar or this other MIDI Sysex Files for OSCar