Gross!! I'd call an HVAC company. I'm sure there will be some heavy lifting involved. :/

I would also call around to different HVAC companies and see what they would charge. They need to make sure that there isn't any rust underneath the furnace. I would also be standing there when they are checking things out, so as to see any damage for myself. Hopefully just a new pan is needed and not a new furnace.

Cut the opposite corners down to the flat section with tin snips and pull out the old pan.(if there is a sump pump setting in the tray If there is a drain in the pan and it is under the unit but reachable from under the crawl disconnect and repeat the step above. Alternatively plug the exit point for the drain and see if it holds water. If it does repeat the process buy use a couple gallons of bleach and let it set for a few days than drain and rinse. repeat if necessary. If none of these methods work the unit will have to be totally disconnected moved out of the way and the pan replaced. Think about replacing the unit with a new system and collecting the available tax credits.