Transmissions aren't my strong suit either, but I think I might be able to help narrow down what's going on.
Does your rear differential look like the one pictured in the link below? Also, 06Leg315 in the thread below is a subaru dealer technician. So I enjoy reading his input on things like this, since he works on and sees a lot of subarus every day.
Or is there fluid coming out from where the axles are inserted into the rear differential, passing by the axle seals (#17) in the first image below? Either way, it sounds like the breather mentioned in the link above might be clogged.
The first image below also shows the location of the breather, #21, and a second image also showing its unfortunate location. I just crawled under my car, and it doesn't look like it's easy to get to..
The link below has an actual picture of what the breather should look like, since I was curious to see how you would go about removing it. I'm not sure if this is the exact part number for your car though, I'm just linking to this vendor for the picture. Even with the pictures, I'm still not sure how you remove it. It looks like you would just carefully pinch it out, since 10 year old plastic might be a little brittle. If one of the arms snaps off, you could probably just flush out the diff until the broken part came out.
And actually, the link below has an even better picture, of the breather sitting on top of a brake rotor.