Recently the heater started smelling like melting plastic, sometimes, and more recently the 1 and 2 positions stopped blowing air. Any ideas?

I tore out most of the dash to see if anything was obviously wrong, couldn't tell. However, I did notice that plungers behind the the glove compartment wouldn't close. It appears to be vacuum actuated. What would cause these to stop moving in and out when changing to feet, defrost, upper, etc?

 

The HVAC actuators are vacuum activated. When they do not move, it is generally because the main vacuum hose under the hood going through the firewall is either disconnected or leaking.
The electrical smell and the heater fan only operating on a few speeds is, unfortunately, most likely the blower motor and/or the ballast resistor failing. Since you neglected to mention what model you have, the 240 blower motor replacement is beyond the ability of the average DIY'r. The 7's and 9's have a blower that is simple to replace.

 

Sorry for not mentioning the model. I have an 89 240 DL. I was tinkering around last night with it and realized that the "plungers" work, I just needed to have the engine on...of course. Sucks to hear that the fix for the heater isn't really a DIY project. Thanks for the help, I appreciate it. Better give my mechanic a call then.

 

Here's Art's wonderful web site where he walks you through the process. What he doesn't mention is the wrench throwing and salty language involved. Check it out and decide for yourself. Volvo 240 Heater AC Blower Fan Motor Replacement

 

if just fan positions 1 and 2 stopped, its possible your problem is with the resistor module on the side of the fan box, or with the wiring. do google '240 fan replacement chainsaw method' for various folks photo essays on an alternate method.