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I'm trying to repair a craftsman 29cc 4 cycle weed whacker I got for free. The fuel lines snapped off so I replaced those and got it to run for a moment. When it does, it pukes oil out of the seal shown in the image below. I can remove the rubber gasket/seal to reveal a phillips shaped hole. Does anyone have any idea why it pukes oil out of here and how to fix it?

https://ibb.co/RPXvpMj https://ibb.co/LhCFHf3

Post the model #. Pull the 2 carb screws and remove black air box housing and carb. Post pic.

Will do. In the meantime, the model # is 316.79184

Here's a closer look at the black air box housing with the phillips hole and the plug I pulled out of it: https://ibb.co/vBwym67

The back of the housing looks like this. The cone shaped piece had an oil line going to it: https://ibb.co/gPrc2YW

The disconnected line here is what I'm referring to: https://ibb.co/0QCN0Yw

Another look: https://ibb.co/QvfK8NX

I'm not very experienced with these sorts of repairs. For the life of me I cannot figure out why there would be an oil line going here, apparently to nothing, which just pukes oil.

That's the breather tube from the breather assy. What that looks like in a tiny 4 stroke - I duuno. Oil from the crankcase is getting pressurized into the valve area and puking out the tube. Worn valve seals? I don't think you can work on valves in tiny 4 strokes. Might as well dig deeper and find where breather tube connects.
Make sure oil is not over full. Being a 4 stroke, if carb needle is stuck open - gas can leak into crankcase.

Just scrap it. The is one those MTD built 4 cycles that simply doesn't oil the engine properly in handheld use. You a worn out PNC which means you will need to shortblock it and the 753-06225 cost about $90 plus shipping if you do your own rebuild of the trimmer.

Personally if you want a good 4 trimmer get a Stihl 4 mix and use two cycle fuel mix. I have seen too many Trobilt, Cub Cadet, and Craftsman 4 cycle handheld to bit the big one because oiling issues.