Like any other troubleshooting problem you need to check things before randomly replacing parts unless you like doing that kind of thing and have the money and like anything else you will need tools to help with the troubleshooting.
First off I would get a manual for your year car as the below might be correct or might not be as the manual I'm using is not the factory one (Clymer manual for 1971-1979 Nova's) but I used it for below and hopefully this helps.
On an electrical circuit you need to start at one end or the other to track down the problem or problems with it. With you saying the horn button does not feel right then I would start at that end and see to see if that is the problem.
Take the horn button off the wheel and test it to make sure it is working. Normally there is only one wire that connects to it and it is grounded through the mounting screws coming in from the backside of the wheel. With an ohm meter connect one lead to the wire or terminal on the horn button and the other to the mounting tab that had the screw in it to hold it on the steering wheel. Now try depressing the horn button. If it is working then at some point when it is being pushed in the ohm meter will read a direct short (0 ohms) or a very low resistance (0-4 ohms). If it doesn't feel right then see why that is and after repairing it use a meter to check it out again electrically. If it's one of those things that cannot be repaired or is more easily replaced then the rest of the circuit still needs to be tested to make sure that was the only problem (and there can be more than one sometimes).
To see if the rest of the system works, take the wire that was on the horn button (making sure the other end it still attached in the column itself) and then touch it to the center nut that holds the steering wheel onto the column. If it honks then the horn button was the only problem and replace or repair that.
If the horn still does not sound then you need to go down to the flat connector on the side of the column and the connector will have about 10 wires in it. Starting at one end there should be a 20 gauge black wire then next to it a 20 gauge pink with double black stripes, and next to it another 20 gauge black. If you take a fused jumper wire and connect it to the third wire from the one end that is the 20 gauge black the horn should blow providing the rest of the system is working and the other end of the fused jumper wire is grounded. If it does then the problem is from that connector towards the steering wheel button and the problem could be in the connector that has the wire attached to it that plugged into the horn button or the contacts inside the column.
If it doesn't sound then the relay under the hood may be bad or the horn(s) themselves may be bad or not grounding good or possibly a wire problem.
To test the relay take a volt meter and on the 14 gauge green wire off of it this wire should show 12V when the horn button is depressed. If not then connect the meter after switching it to the ohms scale to the 20 gauge black wire. This wire should show open when the horn button is not depressed and show almost 0 ohms when it is depressed. If the wire shows close to 0 ohms when the horn button is depressed the wiring towards the horn button is working properly. If not you have to trace back from there towards the horn button to find the problem.
With the plug still off of the relay you can connect a fuse jumper from the stud of the relay to the 14 gauge dark green wire and the horns should honk if they are working. If not then either the horns are not getting power on that wire due to a break in either the wire or a connector, or the horn(s) are bad, or they are not getting a good ground.
If the horn(s) don't make noise with the jumper at the horn relay then unplug the wire off of the horn(s) and test each one with a fused jumper wire between the terminal on the horn(s) and the battery positive post. If they make noise then the horn(s) are good and there is a wiring problem between them and the relay. If they still don't make noise then loosen the mounting bolt for the horn and retighten the bolt as they may not be getting a good ground.
The reason I say horn(s) is I just bought a dealer installed optional horn kit for my Spirit Of America Nova and sometimes the Nova's will have more than one horn installed on them using factory parts.
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Jim
j/k
