The SO recently squired an upgraded refrigerator which was trucked down from another family members house in another state. The fridge apparently worked great before that, but now the water which comes out of the water line tastes weird, mildewy, etc. The fridge states the filter is 'good' or 'green' still.

The only thing I can think of is to somehow run bleach through the internal lines of the refrigerator, but I have no pump or anything to do that and no pressure to press it though.

We can also go out and buy a new filter for the fridge, but that wont get rid if it, right? Any ideas?

chuck existing filter
the refer may have a plug to allow use without filter in place.
unless you are on a well, the city should have sufficient chlorine that after flushing a few gallons & dumping a few trays of ice & then a new filter....you should be good.

If it's really stank- prime the icemaker waterline with some chlorox, and then flush heavily,