What are some ways to remove hardened epoxy from drain pipes

High efficiency furnaces will make condensate. They run the air back through the hot exhaust to get more heat out. This also cools your exhaust enough to use PVC - that's what your upper line is.

In the process of cooling the exhaust, you might get some condensation. Typically that's collected in a little sump tank. When the sump reaches a certain level, a little bitty pump pumps it out - that's your lower line.

If it freezes where you are, you might want to insulate that lower line. If it freezes shut, your sump could overflow in the mean time. It's just a dribble of water, but still. It's a leak of water in your attic.

You probably (and hopefully) have a large amount of sand/grout stuck in the P trap. If so your best bet would be to remove the P trap and give it a good thorough cleaning (out in the yard, with a hose).
(While the trap is off you'll be able to inspect the tailpiece and the drain line as it goes into the wall and clean those up too if necessary.)

If you can't detach your P trap you have a few options:

• If your trap has a cleanout nut, open it up and run water through until gunk stops coming out (you can employ your wire hanger here too, to "encourage" it).
  (My experience is most older pipes that have such a cleanout nut are so old that the thing is frozen and can't be opened without breaking the pipe, so be careful if you try this)
• Remove as much of the tailpiece as you can and clean out the trap with a shop-vac and/or spoon/wire/etc.
• Work a snake down the drain and whip it around like crazy while running LOTS of water
  (In the hope that you'll wash enough of the grout further downstream that (a) your drain runs quickly again, and (b) it doesn't clog your pipes further down the line where you can't get at it.
  This is really a last resort and just delays (or moves) the need for a proper fix...)