First: Have a very direct conversation where you state that after-hours work, and being on-call, are not the job you took. Also state that you really like the job you have, and that you'd like to continue to work where you're working.
Next: Make sure your value to the company is clearly established. What important things have you done that were vital to the company? (If the decision makers think they can replace you, then you're better off switching jobs now.)
Finally: Figure out how to telegraph that you're considering other offers without actually telling anyone that you're considering other offers. In the late 1990s - early 2000s, showing up very late one day in a suit did it. In my case, I just started leaving at random times to meet people for coffee, or taking phone calls behind the office. Later, I didn't pick up the phone for an "important" call with my boss, and his boss, because I was at an interview. They figured it out and the problem was solved very quickly.
You could perhaps try framing it as a negotiation, i.e. "there was nothing in my original contract that indicated this would be one of my regular responsibilities, I'm happy to open negotiations with you in order to add that stipulation." Think of a salary at which you might actually consider being on-call (don't be charitable; make it double or triple or quadruple your current salary if you want). Then, increase that number by 50% and call it your starting offer. If they balk and try to talk you down, offer to go lower, but don't go below that number from the first step. Negotiations will almost certainly stall and your supervisor (who I presume is the one putting pressure on you) will then have political cover to tell their own supervisor (who I presume is putting pressure on them) "hey, I tried", and hopefully this will continue far enough up the chain until it reaches a person that is so detached that they don't really give a damn and drop it. If they do eventually end up firing you over this, then this indicates they would likely have fired you anyway and therefore you've not lost from this exchange. And on the slim chance that they accept your terms of quadrupling your salary, I guess you can retire substantially earlier. :P
> I don't want to have a conversation that way. I shouldn't have to.
I've been though this after a comp review. Despite good review, my raise wasn't impressive. Once I had a competing offer in-hand, suddenly a lot more money was available. Had I wanted to keep the job more, I would have pressed the issue during the comp review, but to your comment, I shouldn't have to.
Having a job offer in hand does wonders for one's communication skills.