So I have to desolder roughly 80 LED's and some diodes.
Here are my suggestions:
1) flux is your friend. If you don't have any, then adding *more* solder is your friend. The new solder contains flux which will help the old solder behave better. Solder tends to oxidize, and oxidized solder just doesn't behave correctly. Like it doesn't melt. Or flow. Flux fixes this, mostly.
2) Don't be afraid to add more solder. Often it's the fastest way to get the old solder out.
3) Gravity is your friend. So is a bit of tapping. Assuming you've cut the led's off the board, try heating the solder, and then tapping the board semi-gently against your work bench while the solder is hot - you'll be surprised how quickly those leads fall out of the hole, and often all of the solder comes out of the hole with it. Just be careful and wear eye protection. For something with two leads, like a LED, unless the leads are crimped/bent, often heating both leads at the same time (i.e. alternating between them) and tapping will result in the entire component falling out.
4) My experience is wick is best for cleaning up afterwards, not actually doing the desoldering. I'm spoiled in that I have a vacuum desoldering iron which sucks all the solder out. Before that, I'd almost always use gravity and/or the tapping method to get the lead out, then wick to clear out any remaining solder.
5) Beware of pad lift, and try to heat the lead/solder and not the board. If a pad gets too hot, it will unglue from the board, and will often cause a failure. Fast work is the best. If you aren't able to get a pad cleaned within a very short time, move on and come back after it's cooled.
6) If you've got a crappy iron, we'll all feel sorry for you (but not enough to buy you a inexpensive but nice iron). If you have a decent iron, try different settings: Too low, and you won't be able to work quickly enough. Too hot, and you'll destroy everything. There's a fine line in the middle.