The age of the fridge may be more than stated, because it was in the house when we moved in 6 or 7 years ago.

The fridge has been acting weird for the last while now, maybe 6 months or a year. Temperature variations, gurgling noises, (more than usual), etc. about two weeks ago, I wascleaning the bottom of the fridge (yes, me, a MAN cleaning the fridge), and I noticed that the liner was bulging, I pressed against it to find that the liner was being pushed out by a water buildup inside the walls. There nust be 10-20 liters of water after accumulating in there! I'm assuming it's been caused by a plugged freezer drain, question is, how do I get the water out of the fridge walls? Will freeing the drain do the trick or is there more to it?

I double checked, that model number came directly off the label inside the fridge, it's a Canadian model if that helps.

I also could not find any info.

The Sears Canada parts site stinks, basically they have no info.
I can tell you that the 970 designates that it is a Frigidaire unit.

Here is a good link with lots of manuals. Join the site. It is free and they do not send you spam. Then take a look at Service Manuals\Free Downloads\ Refrigerator Service Repair Manuals, you may find a unit that is close to yours.
Note: The Frigidaire manuals are with a date range like 5995449906 "Frigidaire Side By Side and Top Mount Refrigerators Jan 2005-Jun 2005 Service Manual" usually just wiring diagrams so check out the other ones.
as there is a limit to the number of manuals you can download per day.

http://appliancejunk.com/forums/index.php

You will have to pull the covers.

If it is fiberglass I would replace it as this will take forever to dry out. I would use styrofoam, if possible.
If it is white styrofoam it also will have to be replaced as this is open cell and will absorb water so it looses it's R value.
I doubt Sears will sell the insulation as a part.

Good luck from another Canuck.