I've been fishing for several years, but have never taken care of my reels like I should. Is oil better than grease or vice versa, or do they need to both be used in combination with eachother?

You need both. Light grease on gears and oil in bearings.

In a sense that's true.  But if the reels are valuable at all, its worth sending them to a pro.

Just adding new lube on top of old can be a waste of time, or actually harmful. A deep cleaning and proper lubing will breathe new life into a reel, especially if it's been a little neglected.

DVT is correct. Just adding to the old grease/oil won't improve the performance much. You have to perform a deep cleaning first before adding fresh lube. And never over lube, this will also take away from your reels' performance. One drop of oil per bearing is all you need.

Kevin