Your profile says you drive an Impreza, so it isn't helping me to work out what kind of engine I'm supposed to be looking at.
My guess is a TDI 130, but it would
help if you told us.
I think I'm seeing the boost side of a turbocharger, with the inlet pipe at the center and outlet at the lower edge (think of how a turbocharger works).
So the oily pipes are boost pipes. The oil is from the crankcase vapours via the PCV system, and is another indicator that these are boost pipes.
There is a joint that looks dodgy, the one between the turbocharger outlet and the first oily pipe. The pipes are supposed to plug one inside the other and be retained by a spring clip that bears against small wedges built into the inner pipe - they should be visible as part of the alloy ring that you can see. This allows the pipe to be pushed into the join and click into place, but you have to pull the spring clip out to free the pipe for removal. The fact that you can see this metal ring at all makes me think that the pipe is well out of place. There is also no spring clip visible (it should be in the groove that can be seen), and it looks as though the o-ring seal is exposed, right next to the cast turbo outlet.
If I'm right, you will have a boost leak from this pipe, and be in danger of a bigger one should the pipe slip completely out of the turbo.
You need to find out why the spring clip is missing. These things don't slip off on their own, in fact they are pretty awkward to get off when you want to undo the pipes. Is the turbo intact, and does the boost pipe still have the locating ears?
At the very least you need a new spring clip. The last of your photo's seems to show one of the ears that the clip bears against, but you need to check all round the pipe and the turbo outlet.
There would be no advantage to going for an aftermarket replacement - this is generally only done to make the engine bay look prettier with coloured pipework, and very few people are going to see this particular hose.
