I've built quite a few log homes over the years and speak from experience. You can contact any log home company via email and get their recommendation on the correct exterior sealant/bug inhibitor. DO NOT attempt to apply drywall directly to the interior logs due to expansion and contraction, as LouisJolliet stated. Any walls built in a log home must be attached to the logs with slip joints, slits are cut into the attaching 2x4 and bolted loosely to the log walls. This includes partition walls and walls that are framed to hide the interior log walls. Because your log home is 24 years old the initial shrinking of the logs is complete but there is always expansion and contraction going on with the humidity and temperature levels.

To begin with,if the logs are not painted or stained I would recommend spraying the logs with Thompson's water seal to help keep out the moisture. As for installing drywall, the application is straight forward. Simply strap the walls if they are uneven or if they are relatively flat you apply the drywall directly to the logs.

You will want to consult a contractor who specializes in log homes. Depending on how they were built, log homes can be VERY finicky because they expand and contract much more than a stick-built home. (p.s. - a 1989-built home is not old.)

Hi
Spraying for termites a must
Stain every 8-10 years
You will need to frame up the walls for sheet rock

For your exterior protection I highly recommend using SIKKENS cetol log and siding products. You can mix this clear product with superdeck for added pigment and to boost the voc's for deeper penetration.
http://www.logfinish.com/store/CetolLogSiding.php