IF it's possible, move your W & D units away from the wall. Be careful of electrical cords AND water hoses. If there's any stress on them, you may cause bigger problems. (As an aside, if you haven't changed your washer hoses in 10 years, I'd do so as part of this 'test'. Be sure to shut the main water supply valve off or the line-valves off before you move the washer.)
Go ahead and then use the units. If you don't find moisture (or if you find LESS moisture on the same wall), then the answer is simply condensation. When warm air (from a W & D unit) comes in contact with a cold surface (the block wall), you get condensation. That could be the cause of your damp wall. You did say it's only behind the units. Also adding to this, cold air (50 degrees) holds less moisture than warm air (75 degrees). Now that it's warmer down there, the walls are much colder, hence, condensation. So again, the cause can be from the temperature change (possibly independently of the W& D).
Good luck! My best to ya and hope this helps.
Jay J -Moderator
PS: I dont think anything is 'drawing' moisture into the basement from the outside.