2001 Beetle stuttering/weak idle and low/no accel

Lets start with the runnability problem, since you already know that it needs an 02 sensor, I would get that replaced, that can cause a lot of runnability concerns seeing as how 02s input to the pcm adjusts fuel to the engine. Now with that said, I'd also take a look at the mass air flow sensor, I have replaced quite a few on this beetle 2.0 liter with the same symptoms as you described, I dont know if you have a check engine light on (I'm assuming thats how you know about the sensor) but a faulty mass air flow sensor does'nt always set a code, But someone with a factory scan tool or similar, that reads live data can look at the MAF readings and compare with specs and see if it is reading correct. Now as for the noise, it could range from control arm bushings, ball joints, struts, sway bar links, etc. The best advice I can give you on the noise is to have a complete front end inspection done looking for worn out suspension/steering parts. I hope this helps, let me know.

Okay. Ordered an 02 sensor last night and will change that when it arrives. Also got some MAF cleaner because it's not going to hurt. I plan to do a multimeter check of the MAF once I dig my multi out of hiding, so if it isn't shot I will clean it.

While I was at my local parts shop I ran another scan on her and got codes P0300, P0301, P0302; all misfire codes. So, mystery sound identified. I had thought it sounded exhaust-y with the popping, but I only drove it for a few minutes with the sound.

I suppose I should look into replacing spark plugs because I can't remember the last time that was done. Is there anything else I should look into re:misfires that I ought to do while I am waiting for the 02 sensor, or is it likely that and/or the MAF could be causing the misfire as well?

Alright, sounds like your on to something, Those misfire codes could be caused by the mass air flow, but now with the added info I believe either the plugs or plug wires could be the culprit, inspect the wires, if they look original I would check on replacing those as well. I have changed a quite a few coil packs on these too, but lets not jump the gun on that, Get her tuned up w/ plugs and wires, clean that mass air flow, change that o2 sensor, and retest operation and see what we got. Let me know.

Well. It seemed better for a bit but it is now bogging down again, particularly when shifting from 1st to 2nd. It is also still quite weak on the accel and seems to threaten to stall if I really press the gas.

The 02 has been replaced, the MAF has been cleaned. I have also replaced the fuel filter and the intake air filter which was a bit dirty. I dunno where to go from here. I really don't want to give up and get gouged but it may be unavoidable.

The only other thing that I know is prone to failure on these that may contribute to these symptoms are the catalytic converters. How the heck can I go about checking that? Or, is there a more likely candidate?