I have a '73 1.7L. I had the PCV hose connected wrong and now the car is burning oil. The spark plugs get carbon build up and causes the car to not idle. Is there a good way to burn that oil out?

I also want to make sure that the PCV hose goes to the air cleaner.

Ok, Not exactly sure what you are asking so I'll give you a few things that may help;
1. If you are dealing with some oil blowby, it is unlikely the culprit of the carbon build up unless it is VERY bad
2. If the car is now running really rich because you have changed the PCV hose routing, you need to figure out the problem and adjust the FI to compensate. the best way to do so is to get a CO meter and then adjust the screw on the brain to lean it out.
3. If you are getting OILY carbon build up, it is likely you are pulling oil through the valve stems or past the rings and you could use a hotter plug to live with it until you rebuild your top end.

Does any of this help/hit the problem?

Where was the hose connected? It goes on the plenum. I don't think the hose hooked up wrong would cause your engine to burn oil. There's another reason for that

I had the PCV hose to the Plenum, but the car died out almost immediately. I moved the hose to the air cleaner and now runs better but won't idle after 20min of driving. So now the car smokes like crazy, which it wasn't before. I assumed that it sucked up oil in the manifold, causing the smoke and carbon build up. My brother had the car before and replaced the rings, but never broke the engine in because he couldn't get it started. Could the reason be the new rings or what?

If the rings were not seated oil will leak past them.