While most of the problems encountered with the overdrive are electric__and easier to isolate and identify__the mechanical ailments require more in depth diagnosis (and descriptions) to zero in on.
Have you individually eliminated__by bypassing around the terminals for testing purposes only__each of the switches? Believe it or not, at least some of your symptoms can be blamed on the gear-lever selector switch; if it's on the very edge of closing the contacts when cold, it may not suffice when fully heated up.
When your ovd. won't engage, do you still hear the solenoid "clicking" into position? Connecting a pilot or test-light into the same connector (at the last junction to the solenoid) will be a visual indicator if 12VDC is being maintained on the circuit.
If all the electrical circuits prove to be functioning reliably and correctly, there's only a few more steps that can be tried externally...
Make sure the pull-in and holding solenoid coils are adjusted correctly__although failure here can usually be identified with melted white & white/purple wires!
You can fit a test-gauge to monitor the oil pump output. Use CAUTION, as the pressures are fairing high if it's working properly (500 PSI perhaps?).
Next likely cause, in addition to those already mentioned, is the degradation of the external/internal friction lining material on the clutch drum. If this was worn thin or breaking up, you'll find bits of it when you drain/clean the overdrive's sump and filter-screen. If yours has the magnets still, check them for metal fragments (there will ALWAYS be fine-fine metal-fuzz particles).
You can try some fresh 30-weight non-detergent oil (what is recommended, though we've all tried others...). Trying 40-wt, or 20/50 (what mine lived on for decades) may make a difference. I'd personally NOT recommend any synthetics or modern "super oils" (in short, anything that claims to reduce friction, as that clutch drum NEEDS FRICTION to work).
If none of that gets you anywhere, it'll probably have to come out for the further inspection of internals.