Ok, used Lightning drain cleaner (thanks for all the suggestions) and got the clog out now I have sprung a small leak in the fittings under the bathroom sink. Leak might be from the acid drain cleaner but now I need to replace a jury rigged trap hopefully with a conventional set up.
This is what it looks like now.

The leak is at the bottom of the straight run down from the sink on the left. The screw on compression fitting at the top is also cracked (where the sink connection hooks to PVC). The bottom (at six o'clock) of the fabricated elbow seam appears to be tight but I want to replace that with a conventional PVC trap and then hook to the drain pipe going out.
My question is "can I do this all with PVC compression fittings and new PVC trap or do I need to keep the same crappy design that exists now. The existing is all done with 2" PVC. The fittings where it joins the elbow coming down and to the drain have been glued and I think are so tight to the drawer (on the left) that I might not be able to actually tighten the fittings by turning. Back drain section looks like this.

Could I do it all with 1/12" and not 2" and gain some clearance? Guess I'll go to Lowes and show the plumbing guy the pics and see if they can give me whatever I need to get the job done this Saturday.
Any suggestions or recommendation on a parts list would be appreciated. I'm hoping to avoid going back and forth from hardware store since it's an hour away. Maybe someday we'll be able to use the bathroom again, at least we have the shower back in use.