02’ shudders when accelerating

Greetings!
My beloved 02’ v6 is getting up there in miles, 334,000 and change.
While driving, it has a significant shudder when i touch the gas. It does it from a dead stop and again at about 50mph
There is no check engine light. my wife drove it to town, check engine light came on so she had Oreilly run the code..
P0301 cylinder 1 had too many misfires in a predetermined amount of time
Additional diagnostic trouble codes P0300 Random /multiple cylinder misfires detected..
Possible solutions: valve cover gaskets, plenum gasket.
Driving home the truck stopped accelerating while jerking bery badly, she parked it at a church. Im going now to tow it home
What should i look for? How to correctly diagnose this problem?
Possible addition damage to look for?
I just replaced my radiator, when the radiator drained the coolant the truck overheated and died a couple weeks ago but ran fine after cooling down..
Also a couple weeks ago i got a code, don’t remember the code number.. suboptimal catalytic converter reading. It went away on its own. Not sure if these are related or point to a specific problem..

thanks for any helpful advice!!

 

Do a compression test first. If she isnt sound mechanically anything you do to patch it will be a waste of time and money.

The OBDII system operated as designed, there is a threshold of misfires that has to be exceeded before a check engine light is illuminated. Everything before that sets a pending code. Misfires happen more than you know, the programming in the PCM that the Clean Air Act mandates is that any condition that increases emmission 25% more than normal sets a CEL. This can mean anything from a cooling issue to a transmission issue.

 

Do you hear a little low metallic rattle sound after you turn start it up, coming from underneath, on the right hand side, but doesn’t last more than a minute or so? If so, then it’s the catalytic converter.

 

Thank you so far.
The day it shut down it idled at around 600 rpm from a cold start. Usually it idles around 1,500 rpm until it warms up. Does that also point to catalytic converter or something else?

 

I finally got around to starting it up.
It was slow to start and a little jumpy,
Once it cranked after about 20 seconds if trying it seems to run ok but there was white smoke coming from the exhaust briefly.

 

I’d follow @Glamisman advice and do a compression test. I’d also be ready with a fresh set of spark plugs as that could be your issue and you’ll already be in there. Have you been monitoring your coolant levels?

 

When the radiator was leaking we had to drive it more than we wanted so we added water to the radiator every time we stopped for about a week. Ill advised i know, gotta do what ya gotta do