Engine light on, rough idle, code P0304

I have never heard of an EGR causing a misfire code. When you changed the spark plugs, did you change the coil? I would bet that the coil is failing. What you need to do is get a spark strength tester and check the sparks coming from the coil to the spark plug.

With the engine off, you will unplug cylinder four's plug wire, and connect the tester to the spark plug on one end and the wire on the other end. Start the car and observe the spark. Turn off the car, and run the test on a cylinder that is not having a misfire code, like number one. Compare the spark color and frequency. Blue sparks are stronger than yellow sparks.

This is the spark tester that I use: https://www.amazon.com/Lisle-20610-Inline-Spark-Tester/dp/B0002STSC6/ref=sr_1_3?ie=UTF8&qid=1497320343&sr=8-3&keywords=spark+tester

Would a failing coil cause such a rough idle?

Yes. It could be putting out weak sparks.

I will buy a spark strength tester and let you know what happens from there.

Okay good.

The spark was yellow. So should I spend the money on a new coil pack?

Did you check another cylinder to get a base line?

So all of the sparks on the cylinders were orange, but cylinder 4 was lighter. I am not sure what to do now.

If it was definitely lighter than the other cylinders then I think that you just need a new coil. Simple as that.

replaced it. seemed to have calmed the rough idle. I'm guessing I need to clear the code so that my engine light goes off?

You can clear it or just keep driving it. If the problem is solved then it'll go off by itself within a few days. I'm glad we got it figured out though.

We cleared the code, but the engine light is back on with same code: P0304. Could it be fuel injector?

I'd put a tank of premium gas in it, a fuel additive (Lucas makes a good one in my experience), clear the codes again, and drive it a few days. I know it's an unconventional answer, but it's worked for me in the past

Went to drive my car today, waited for cars at a stoplight for about 1 minute and a half, engine light began flashing. I haven't put a fuel additive in there, but can't imagine that would solve the problem.

Flashing CEL means it set a new code. Have you scanned it yet?

Just to review, you've already done the plugs and coil so far. What plugs did you use? On a lot of cars, using plugs that aren't stock (ex. Split fire plugs) can cause more issues than they solve. Let me know.