Ron sounds a little frustrated himself, so I'll chime in. Basically you need to understand the relays better. Use a multimeter to make sure you understand when the relay is open and when it is closed. i do this by using some leads from the battery, I attach leads where I think they should be, mimic the action of the switch (in the case of the horn this is a switch that grounds) and see if I am getting voltage where I want it. I then use this information to install the relay. It sounds like you you think you wired it right, so my explanation is that you have the plug i.d. mixed up, or if all else fails you have bought defective relays (I doubt it, I use Ford type relays as they are cheap and seem to last). Finally, I still have the old round relays in my 220 and have never had a problem with them, this begs the old adage "if it ain't broke..."
Check out the link that Ron gave you, it is well laid and pretty much explains as much, if not more, than I know about electrics, and I can wire/diagnose anything on a 120 and have been known to successfully take on much more complex vehicles. It's a bit steep a first but the learning curve in auto electrics flattens out fairly quickly, a few Eureka! moments and it all becomes old hat.