Multiple codes.. please help

Why do you think it's fuel injector related? Ohming out ignition coils isn't going to tell you anything - unless they are completely open or shorted. You'd have a definite misfire that you would've easily found. If you can smell gas while you were trying to start and run the car; that kind of rules out injector and fuel pump issues. Reverse the order of the coils to see if your problem moves - that should isolate a coil issue.
Pull the plugs to see how each cylinder is burning, they should be uniform in color and consistency. If your using crappy Bosh plugs; go back to ND or NGK.
My ignition coils began failing on my GMC, one at a time around that mileage. I had to wait 18 months, for the coil to completely fail, to find it. Every-time it misfired, I'd pull over to try to find it and it would go away. No CEL, but a definite loss of power and I can feel the misfire. When I started getting another intermittent misfire after changing the first dead one; I replaced all of them - no more issues.

Check your engine compartment for a nest and chewed wiring harness

Hope this helps...

 

keep your eye on coolant level. is the oil creamy at all?

ever cleaned the egr circuit?

 

And, is there white smoke spewing out the tail pipe when the engine runs?

 

50k miles....just about the perfect distance for chinese counterfeit spark plugs tips to be disintegrated...

it would be worth checking them

a good iridium plug should still look practically new

unfortunately, this:

startup (cold), rattle, shake engine noise. Codes: P0300, P0301 and P0302.

in a Gen 3 seems to commonly be due head gasket problems. hopefully not for you.

 

Bisco these cars rarely if ever leak coolant into the oil. They leak into the cylinder when cold causing the plugs to foul and misfire. If it clears and runs fine in under a minute it has the dreaded gen3 hg cancer.

 

Mark coolant level with marker or tape.
This is most likely the Dreaded Head Gasket.
It's the perfect mileage for it.
It's almost guaranteed to blow on your engine.
Mine and many others have.
Rattles then clears up is the head gasket.