New (to me) Washer and Dryer

Hooray I got a washer and dryer.  Thanks so much to Joseanne who decided she wanted stackable washer and dryer and was nice enough to give me hers.  So I hadn't done laundry for two and a half weeks knowing that I was getting a washer and dryer.  So anyway, we got them up our rickety stair way and hooked up and I was so excited to wash some clothes.   I put in my first load and i was doing some miscellaneous things around and about when I heard water being poured all over the floor.... I guess our drain doesn't drain fast enough. I thought it might be clogged but DrainO didn't do anything.... So I ended up spending the rest of the load turning the washer on and off and on and off again and again so it would only drain enough at a time so it wouldn't keep over flowing.... that lasted till 1:30 (because I HAD to do 2 loads so I had clean clothes for my job interview tomorrow) well at 1;30 (yes in the morning) our downstairs neighbor came up and said that the she was sleeping when she heard drip drip drip in her laundry room... yes we were leaking into her laundry room.. I guess the people who lived here before had the same problem and the landlord came and had to unclog the drain.  So we called the landlord this morning and he had a stroke and is in the hospital, but his wife said she would have her son come look at it sometime today... but it is 9:30 and he hasn't shown up... Any ideas?  Anyway I am done blabbing, here are pics of my new washer and dryer

Dryer (its pulled out so we could pull the washer out to check the drain) washer in the background

Washer also it has to face sideways in the laundry room, which is a little weird but still okay.

The drain that keeps overflowing... not a great pic but still a picture

Anyway thanks for reading... any advice let me know