Endless problems with air and exhaust, throwing codes, please help

Hello, I own a 2003 Tacoma Pre-Runner 2.7 l standard cab, 178k miles.
So far, I've cleared two codes it had, and now I've got a 3rd one I guess I'll have to throw parts at, too.
It was my dad's truck, and he was pretty rough on it and did some pretty weird work to it, which I'm still fixing.
So far, I've replaced the A/F sensor (about to get to why I didn't replace the downstream o2 sensor just yet), put in a new PCV valve and fuel filter, and replaced the MAF sensor as well as its connector with new ones, I wish I would have taken pictures of what all was in there before I got ahold of the truck.
Checked all the vacuum lines, they seem to be fine.
My dad says he got a new catalytic converter put in, which I'm pretty sure he's referring to the rear cat, because I'm fairly certain it has the wrong part in there.
It's got a sensor on it that the wires have been cut off of and there is no loose connector thst I can find.
Which is why I think it's the wrong one.
It does have the o2 sensor after the cat hooked up and everything, though.
But that extra sensor is still on that cat, just hanging out I guess.
The code I'm currently having an issue with is p0420.
I'd just replace every component of the exhaust system if I had that kind of money, this is getting frustrating.
I've lurked on this site for quite a while, but now I need some help that I can't look up the answer to.
This is my first Tacoma, I haven't even had it for two months now, but I just want to fix the problems it's having, and I live in a state that has emissions, I've gotta get it fixed soon.
Please help me! Thank you

 

The extra downstream sensor can be replaced with a plug if you can find the right size and thread, as you only need two in total, upstream and downstream.

Please see this for a PO420 work around, this may work in your instance? Good luck!
https://www.tacomaworld.com/threads/rear-o2-sensor-bypass-cel-fix.325297/page-5#post-13192072

 

I've heard mixed things avout bypassing it, I just went ahead and ordered a new rear cat and downstream o2 sensor from rockauto, I really don't want to keep driving it around with the wrong cat in there.
And I know who put it in there, I don't feel bad about correcting this issue with a whole new part, lol.
Hopefully this will do the trick, I'll update my results after I get the parts in and installed.
Thanks

 

So after I got my new rear cat shipped to me, I got ready to install it, and realized that the guy who "fixed it" before me welded it to the "front cat", which just looks like a universal catalytic converter, welded to some pipe.
So, now I'm waiting on the front cat.
Luckily that guy didn't touch the manifold or the intermediate pipe.
This is gonna take awhile to fix...

 

Fun, this guy wasn't 'Dad' was it? Lol

 

No, but it was one of his buddies, lol

 

Now I'm getting a p0136 code, I replaced the downstream o2 sensor just this week.
Hopefully after I get both of the new cats in it will help with all the codes it's throwing at me, and btw, anyone know what relay the o2 sensor is connected to?
I may just go ahead and get a new muffler soon, would that be part of the problem with it running too lean?
This truck is going to give me an aneurysm, lol

 

A Po136 can be caused by exhaust leak before rear sensor and after front sensor. And it doesn't have to be a big leak. Been there! Had tiny leaks at rusted little welded heat shield by rubber hanger. Ground it off and put an exhaust band clamp around leaky area and FIXED!

 

That's a definite possibility, I think after I get the new correct cats in there that won't be an issue, I'll check for any other leaks afterwards, too.
I went ahead and ordered new vacuum lines and thermal wrap for the headers, why not.
Hopefully it will be running at top notch soon, as long as I don't find any other horrible hack work on it, lol

 

Update: after replacing both cats, after 2 days of driving, NO codes are being thrown (yet). So far so good

 

Saweeet. Fingers crossed.

 

It should be pretty easy to identify a catalytic converter issue. You'll need a temperature gun, if you don't have one they're quite useful as a diagnostic tool, and get vehicle warmed up. Shoot both cats and the temp of front closest to engine should be hotter than the rear one. Also, if you have an internal leak of anti-freeze or motor oil the converter will have a contaminated substrate and it won't be doing its job... triggering sensor (s) to a CEL. A lot of different companies sell after market cats but other than the over-priced Toyota, the MAGN-FLO has the best success rate over time.Good luck.

 

Thanks for the info, and I do have an infrared temp gun, I'm a commercial/industrial electrician. I'll check out the cats soon.
I know a big problem was the jerry-rigged job on the cats that were in there, I could clearly see holes in the welds.
I'm pretty sure the headers have got a leak in them somewhere too, but working two jobs and going to school limits my free time to work on the truck like I want to.
I just drove about 200 miles yesterday down here to see the family in AL, no CEL so far. It was going off fairly quickly whenever I had reset it before, so it's doing much better with the new cats in there, that I do know.

 

Oh, and I got the Walker "ultra direct fit" cats, I've heard good things, and they seem to be doing well.

 

Update: so far, so good. No CELs, but it is still running a bit lean, just not enough to throw a code.
Only issue I can notice is timing. I took a screenshot of my OBD2 reading while the truck is on, and then another after I cranked it up.
Any ideas?
Seems to be running fine, though I can hear it "ticking" a bit.