I was replacing my torsion (anti-sway) bar yesterday and I had to break this black line that I am pretty sure was the oil pressure sending line because it just looked like it. Anyway, will leaving this cause a big problem because of the hole in the system? Should I get a new unit or can I just cap it with one of those cap nuts?

I do not know what year and model you have; but any car with a busted Oil pressure line is going to lose a lot of Oil if nog blocked or replaced.
When you are stepping on the accelerator and the needle on the Oil Pressure Gauge is up to 3bar your Oil pump can actuall put out over 100 psi. At this pressure alot of oil can come out of a tiny hole.

Plugging it off will not harm anything assuming you do a good job and it stays plugged.The other exception is that you will no longer have a working oil pressure gauge so if you were driveing and your Oil Pressure did fall you would have no idea at all until it is too late.
A new Oil Pressure Gauge tubing from an internet seller is in the $30-$40 range plus shipping.
Or, get one from the Junk Yard and hope it is OK.

__________________
84 300D, 82 Volvo 244Gl Diesel

A "big black line" in a Mercedes would be part of the power steering, transmission cooler, or engine oil cooler circuits. Leaving any of those unrepaired would not be recommended.

__________________

"Buster" in the '95

Our all-Diesel family
1996 E300D (W210) . .338,000 miles Wife's car
2005 E320 CDI . . 113,000 miles My car
Santa Rosa population 176,762 (2022)
Total. . . . . . . . . . . . 627,762
"Oh lord won't you buy me a Mercedes Benz."
-- Janis Joplin, October 1, 1970

Whether it's a big problem or not depends on whether or not the engine is running!!!

I have a 82 300D Turbo. The black line runs into the interior along with a bunch of vacuum lines. I broke it right at the base, so the whole line is still there, just not connected.

I want to get the car running this weekend so I think I will cap it for now until I can find a replacement.

How will you accomplish the "capping" task? As previously mentioned, the oil pressure line is subject to significant pressure, greatly exceeding that displayed on the gauge. A "duct tape" solution isn't going to be a viable one.

Does one end of this mystery line attach to the oil filter housing?

I would cap it by using one of those covered nuts. 100 psi would burst through duct tape in no time, and I know that. Yes, the broken line was supposed to go to the bottom of the oil filter housing and that is why I thought it was the oil pressure line. The other end goes into the interior.