Greeting everyone!

I was enjoying my Crossfire (2004 NA 6MT) today when I looked down to see a check engine light! I honestly don't know how long it was on for, as the cruise control lever perfectly covers that area of the gauge cluster!

Anyways, I drove the car to my local Oreily's and scanned the codes. They came back as follows:
P0304
P0306
P0301
P0300

I was really confused, as the car is driving completely fine, both before and after reading the codes. I would have never guessed it was a misfire issue.

I plan on cleaning all of the connection points for the engine wiring harness, but wanted some advice from the more knowledgeable here.

What should be my next course of action to fix my issue if cleaning off connections doesn't work? How can the codes pop up when the engine isn't bogging or running rough?

I noticed a somewhat foul smell coming from the car recently, but I'm pretty sure it's either my brakes or my clutch, since the car hasn't been driven for years before I got it.

Thank you everyone for your help! I look forward to hearing any suggestions that may solve my problem!