Just saw this. I often have to recreate sounds for cover bands I play in. Usually what I do is look at when the song in question came out, subtract several months to a year to factor in when the track was recorded, and see what synths were available at the time that could have come close to making the sound(s) in question. The older the song the easier because once you get back to the time before romplers, everything was some kind of analog or early FM concoction. Being as how this was Styx, one of the biggest arena rock bands of all time. If the song was from their heydays it would be pretty easy to deduce what they had at their disposal. There's probably no single answer because they would have had access to any of the then "modern" gear that they wanted.
I'd focus on the song you want to try to recreate and see if you can find a bootleg video of a concert online where they played it live and see if you can get any info from that. Short of that, you'll have to do the sleuthing. If it's the mid - lat 70's then it's going to be a fairly safe bet you're hearing a Moog Mini, Oberheim 4-voice/SEM or even an early OBX or Sequential Circuits Prophet 5 in the track. That along with the usual fair of Rhodes, Organ, etc. I've always liked Dennis DeYoung's synth textures. He's an amazing song writer but highly underrated as a synth orchestrator.
