What are good general strategies for Pandemic?
A few points:

Movement is usually the most expensive action. Sure, you're getting closer to be being able to do something useful, but the moving itself isn't technically doing anything - it's just using up a turn. Because of this, if you go to a city with 3 disease cubes on it - strongly consider clearing them all off. If you don't, it just means you'll need to return sooner, and waste more turns getting there. The exception is late in the game - you're probably safe reducing it to the point where it cannot outbreak (ie. when there are two Epidemics left...you only need to reduce a city down to 1 disease cube).

When you have an Operations Expert in play, build research stations liberally. There are lots of instances where you can save someone else 2 (or many more) actions at the cost of building 1 research station with an Ops Expert. Even something that seems like a 1 for 1 tradeoff is probably worth it, especially if your Ops Expert doesn't have any pressing needs. Late game, you might be able to save someone who has a cure (or is about to have one) 3-4 movement actions that they would have needed just to get to a research station. Build a station in the city they are already in.

I used to place one research station in the middle of a problem area, then fan out from it to clear the surrounding cities. Now I build one station at either end of a problem area, so I can enter on one side, sweep across the problem cities, and leave from the other side, without having to backtrack. (But don't leave huge gaps - I'm talking like: research station -> city -> city -> research station)

This might be obvious, but pay attention to how many cards of a particular color you've already played. Later in the game, you'll have to make decisions about which to keep. Keep the colors that you've discarded the most of, since there are fewer of them in the deck.

And when deciding what to keep: I used to think that it made sense to keep the cards that are furthest away from existing research stations. Now, I believe that it might be better to keep cards that are closest to research stations, since you'll be able to quickly get to that area, and you'll probably be there often since it's a problem area, you can use those cards for charter flights - which offer greater flexibility.

Also, wait as long as possible to make the decision of which color to go for (since you'll have to discard so you don't go above 7). If you have 3 red and 3 blue, don't even think about picking one and discarding the other. Get rid of whatever the 7th or 8th card in your had is. Even consider using a special, that is if it will provide a solid benefit at that moment. (An exception would be if another player has 4 red or 4 blue - then you know that they will be curing that disease, not you - so you'd probably rather keep those 2 yellow cards.)

I know I said movement is the most expensive action, but getting together 5 of one color is probably worse. It takes a TON of move actions to use the Share Knowledge action.

That said, if you have the Researcher at the start, find someone with two or more cards of one color, and give them more of that color. This will be the easiest chance you'll have the entire game to use Share Knowledge.

As for eradicating - I only do it if I can guarantee eradication in the next two player turns (using all 8 of their actions). No scientific basis for that really, but it's something that I have to be able to almost guarantee, given the state of the board (where an Epidemic is unlikely, or unlikely to stymie the attempt). The number of movement actions this will save you down the line is massive. This most often happens with the Dispatcher, Medic combo you mentioned. Also, don't eradicate late in the game (unless it somehow won't negatively affect your ability to cure the other diseases).

Plan ahead as much as possible, but be wary of Epidemics. Don't plan out 4 player turns ahead if an Epidemic is probably going to happen before then. Having a long term plan get interrupted (because of a new emergency) can be devastating.