I live in WV where the temp has been single digits the last few days. I did the dishes, then went to do a load of wash, and the rinse cycle started to kick the water into the kitchen sink. We followed our landlord's advice, using draino, vinegar, baking soda, and hot water to try and flush it out. We plunged both the washer outlet, and the kitchen sink (which is a double). All that did was switch the water back and forth between the sink and the washer. To make it worse, the pipe under the kitchen sink where it joins with the piping under the house has a leak. There is no seal, only caulk ( a DIY job obviously) which has started to come loose, resulting in water all over the floor. This morning, the washer outlet water will not move.
The stats on the house according to our landlord is that the scullery (Kitchen and laundry room combined) was an addition from the 50's. It has no basement, and PVC and copper piping for the sewer line with little or no insulation. We believe that is a blockage of some sort causing this, but are unsure if it is due to frozen pipes or an actual blockage, or what. The bathrooms are working fine, so we are scratching our heads. If you have any advice, please let us know.

If the drain line's froze try pouring boiling water down it. If it's clogged then snake from the washer or kitchen roof vent. Good luck, Tom