Don't try to hook them all together through Y-cables or the like, that will cause problems. You could buy or build a selector switch, find a nice rotary switch, project box and the types of jacks you need. Could even add some audio transformers for ideal impedance matching. Would be a fun afternoon DIY.
I use an inexpensive audio mixer as it provides a headphone connection. It also allows me to listen to music from the computer while monitoring a local repeater, then hit the mute button on the PC's input if there's chatter I want to here . Each device can be connected to it's own channel and levels set individually so you don't get blasted. It also reduces wear & tear on your rig's volume controls. You can likely find a Behringer from Guitar Center for ~$50 with all the inputs you'll need.
If you're fortunate enough to have rigs with line-level outputs, use those! If not, your next best choice is the headphone jack and set the rig's volume low. Otherwise use the external speaker jacks and keep the volume down so as not to overload the mixer.
Impedance matching here isn't as critical as in an antenna system, microphone input or high-powered audio systems. Your rig's internal audio amplifiers are likely expecting a speaker from 4-8 ohms, whereas the line-level inputs of a mixer are likely to be at least a few kilohms. Your rig's headphone outputs are likely expecting 25-100 ohms and output a lower level, so use those if available. Either way, the typical audio amp in most radios is perhaps a few watts at most. Presenting them with too low an impedance could cause damage, but a higher impedance load just means they'll output less power.
In short, I've run dozens of radios like this over the years and haven't screwed up anything yet.