I have a 23 year old Eljer toilet that has recently started clogging up
badly. I plunge it, it flushes normally with water, then clogs up
immediately. It is getting tiresome.

Any idea why I am suddenly having this problem and what I can do about it?
I have a toilet auger, but if it flushes normally with water, then I don't
see that it would be useful; and it is such a job to dry (My sons swear
that nothing improper has gone it it...)