Horn doesn't work with car on, but does work with keys out of ignition. any help?

The relays wouldn't have anything to do with the problem you are having. You have described a possible short in the wiring system. What you should do first, is check all of the fuses in the car(under or in the dash board & also in the engine compartment) and see if any of them are blown. If so replace them then try the horn again. If you don't find any blown fuses, the next thing would be: Did you have any electronic devices added to the car that were not original to it? Such as a stereo upgrade or swap? If yes, check all the wiring, because the add on was probably wired into the horn system and is shorting it out, so undo all wiring connections made for the add on, then try the horn. If it works properly, when you rewire your add in, find a different wire source for it. Next, there was a massive recall for Honda and many other cars for faulty ignition switches. Check with Honda and see if you car was included in that recall, if it was but you never had the repair done, get it done. If all that fails, you need to have the car checked under the steering wheel. There is a piece of metal that lays under there and it conducts electricity to various options that work via the steering wheel & steering column, such as horn, blinkers etc.In most cars, they call it a clock spring. Some manufacturers have had recalls on these as well but I do not believe Honda is one of them. I also don't really thing your problem is in the clock spring, because the horn works when the car is shut off, so that would point to one of the other causes I mentioned. Keep us posted.