Replaced both coil packs. Replaced coil housing. Good compression all the way across. Replaced spark plugs, but misfires badly.

injector or valve train

Timing could have jumped. Could be a bad head gasket also. even possible to be a small hole in piston check the cylinder for compression. Check the fuel injector to that cylinder if you have bad air to gas mixture it will throw a code of misfire change fuel filter check fuel injector to see if clogged. most likely it is the fuel injector .

Fix your (P0304 misfire on cylinder 4) first. Start at spark plug and work your way back to coil. Run it for a couple of minutes and pull the spark plug out and inspect.

Is it wet with fuel and oily? Smell it too! If so, the misfire is probably caused by lack of spark (or sufficient spark) and your problem lies in the ignition system - (ie - bad plug, bad gap on spark plug, bad plug wire, bad plug boot, bad coil, bad coil pack, or maybe just a loose connection.).

Is it just oily? If so, you may be having a compression problem. Check compression on Cylinder 5 against compression on a known good cylinder. If you have significant (15+%) lower compression than a good cylinder, it could be a valve (intake or exhaust) sticking or perhaps a bad cylinder. Pour an ounce of motor oil into the spark plug hole - wait a minute and do another compression check. If the compression is raised for a moment, you probably have a piston ring thats worn out. If you have no increase in pressure, it is likely a stuck/sticking or broken or burnt valve. Either of these is not very good.

Here is a link to spark plug inspection: http://www.aa1car.com/library/reading_spark_plugs.jpg

Again, fix the misfire condition first. The other codes may clear up after some driving with all cylinders firing correctly. Driving with misfire(s) for a long time can lead to other significant and perhaps costly repair problems.

The plug wires could. if it a 2.2 if it's a 2.4 bet on the coil cover,
the big plastic piece that houses the coils.

Not sure, but may be the timing is off. Autozone should be able to check it with a timing light. The timing setting determines the firing of the spark plugs. It it is off, it doesn't matter how new the spark plugs are.

you need to determine what cylinder is misfiring first then do compression and leakdown test if the parts you put in are in correct misfiring cylinder you possably have a bad valve or burnt piston

The coil pack on these engines runs hot, so it's important to make sure there is heat sink grease under the coil to transfer heat. If the coil module gets too hot, it will fail.
If an engine is hard to start or has a misfire at higher speeds, the problem may be a weak coil, a bad plug wire, or a fouled or worn spark plug. On 1996 and newer vehicles, you should get a cylinder misfire code. A code for one cylinder would likely indicate a fouled plug, bad plug wire, or possibly a clogged or dead fuel injector, or a compression leak (burned exhaust valve). Misfire codes for two cylinders that share a coil would likely point to a bad coil.
Another way to figure out if a misfire is a bad coil is to swap two of the coils on the coil pack. If the misfire moves to the new cylinders, the problem is the coil. If the misfire remains in the same cylinders, the coil is OK and the problem is the wires, plugs, injectors or compression.
If you test a coil with an ohmmeter, the test specs are 0.5 to 0.9 ohms for the primary terminals under the coil, and secondary resistance of 5,000 to 8,000 ohms at the high-voltage terminal.

A misfire doesn't always have to be ignition... it's just the most common cause. Faulty or plugged injector, low compression. You need to check fuel pressure and test the fuel injector flow. Then check compression. If you don't have tools for these tests, take it to someone who does. Testing is much cheaper than throwing parts at the problem.

It sounds like a misfire. Check spark plugs 5 and 6. It could be bad fuel, bad plug wire, or weak coil. Check the fuel injectors as well. Other possible causes could be an egr valve stuck open, vacuum leaks, low fuel pressure.

One often overlooked item is the spark plug leads themselves! They don't last forever - Some start breaking down internally after only a couple of years, and although you still get a spark at the plug, it is not a very healthy spark.

If they haven't been changed, it is well worth giving it a go.

Hope this helps!