Ok just had a look at the diagram in the Hayned Manual, there's not a lot to the horn circuit and I think the ABS light is a seperate fault. If the relay clicks then power is reaching the relay from the column switch, so you can count out a problem there. The relay itself could be faulty, you need to pull out the relay and check for 12 volts at terminal "30" (in the socket where the relay fits). If you have 12v there the problem is the wiring from the relay to the horn itself.
When you checked at the horn for voltage, where did you earth the multimeter to? Was it the horn connector or a metal part nearby? If it was the connector then try another earth (ground) maybe the earthing is bad.