You didn't mention if this is an automatic or a manual, although the other replies seem to assume it is automatic. My '83 240DL has had on-and-off overdrive problems since we have had it, about 10 years. The most common problems for us have been are:

1 - Loose wire (or entirely fallen of) on solonoid. The wire is just a spade-terminal on the side/bottom of the tranny, and can easily get pulled off by a stick, or rock, or just vibration.

2 - OD Relay, hidden behind and to the left of the glove compartment. Some of the circuit board gets kind of deteriorated, but can be fixed with a soldering iron, or a few dollars for a junkyard replacement.

3 - OD button on the stick shift. This only broke for us once. Got a new one on ebay for $1.

4 - Loose wiring inside stick shift. Just had to pull it back up and give it a little slack, so it wouldn't pull on the button connectors.

5 - Cold temperatures. When it is cold (freezing or below), the OD does not work until the tranny heats up. Usually takes 15 min of driving or so. This one is unsolved, but is likely related to...

6 - 4th gear sensor inside tranny. There is a little switch inside the tranny that closes when the stick is in 4th gear. I often have to (especially in the cold, but sometimes just randomly) push the stick shift as far to the bottom right as I can. I used to put a bungee-cord on the stick to hold it there. I think the switch is just all gummed up or something, and doesn't want to close all the way. I think the hot tranny makes the gumminess go away.

We once had to drive from NC to NY with no OD. We didn't go over about 60, which in VA means getting run off the road, but otherwise is not so bad.

-Kevin