So 2 part question, let me answer both separately:
1. What if you play a gig and play re-edits:
Here the same rules apply if you would play the unaltered version of the song. You are playing out someone else’s work. Which means the copyright owner or copyright governing body has to get money for that. You are however in luck that in 90% of the countries out there THE VENUE OWNER or MANAGER is responsible for paying this fees. To be on the safe side include in your contract for the gig that you assume that the venue owner takes care of paying said fees. Check out some freely available DJ contracts on the internet you will find many with that passage in them.
2. Putting your re-edits on the net or even sell them:
Now that is completely another story and very complicated as often the holder of copyrights is different from the author or musician/producer, especially in the EDM scene. Best bet would be to contact the relevant rights owning body, but many times this is unclear. So you can also try to contact the label that release the song(s) and try to figure something out.
HOWEVER: Many times in the EDM scene this is very hard as some of those rights owning companies are just money hogs and want a fee upfront that often exceeds 100,000 dollars and a share in the sales. What you should go for is only a share in the sales, but you will need at least a lawyer and an agent to deal with that stuff, as working with “not your own stuff” is a hard thing.
An alternative to that would be:
Try to hookup with totally independent artists via soundcloud or youtube and ask to make remixes for them. If they grant you permission, then you often get out of it no payment at all. If you make some sort of a name for yourself the above will be much more accessible and easy as you can show to them a body of work and your agent will have much easier negotiating.
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