Hi Skiroy,
Well the first obvious question is, what's wrong with the unit? If it's working ok, no need to fix it.
About the psu: if the voltages read ok, it doesn't mean it's functioning properly. What you measure is DC (rectified) voltage and what's causing noise and such is AC ripple (most of the time). This can by caused by old, dried out, capacitors. As they are not that expensive (get Panasonic NHG's or FC series with same voltage or higher) I choose to replace them just to be sure but if you want to be sure you can check te power lines for ripple using an oscillocope.
As for the capacitors on the voice cards. There is no absolute need to replace them but as I'm replacing all the tantalum caps, replacing these isn't that much of a deal and they are around 30+ years old.
Troubleshooting chips can be hard, depending on what type of the chips are. Broken opamps can be found by tracing a (test) signal with an oscilloscope.
Finding faults in logic chips, of which there are plenty in an OBXa, is a lot harder. Determining where the fault in the logic chain is (which buttons are not functioing for instance etc.) is a first step. You can then trace this fault on the schematic to see which chip(s) might be faulty and then somehow check these chips on the pcb. A tedious task!
The OBXa is a complex beast to tame and in al honesty not really a newbie project...
Good luck!