Not easy to diagnose this from a distance but the first thing to say is, don't try to put it into reverse with the engine running, if the OD is still engaged, otherwise you will seriously damage the gearbox and/or OD. You say that the solenoid is "working", so can you feel it clunking back and forth if you hold the solenoid body? The valve that the solenoid operates can stick, and this leaves the OD engaged. This usually bleeds down when left parked, say overnight, and you can then carefully try to get reverse with the engine off. The smell may have been the OD clutch if the box and OD oil level is very low and certainly the OD will slip in and out if there isn't enough oil in there for the pump to keep it engaged. The smell could also possibly be from oil being burnt from a sparking loose connection on OD switch on top of the gearbox.
So, two possible options could be low oil or bad connections to the solenoid, which could itself be sticking or faulty. Oil leaking into the solenoid can cause it to lock hydraulically even if it's OK electrically.