The previous owner of our house made the garage a den and added a garage off the den. Because the washer/dryer were in the original garage next to the w/h and electric panel, along the back wall, he just moved the washer/dryer onto the back porch and built a small closet around the w/h & panel. I don't believe code will allow us to "squeeze" the washer/dryer into the small closet because of the elec panel and we don't want them on the back porch. We thought about just putting up walls around the washer/dryer, but there is still the issue of having to go outside to wash clothes - any suggestions for a low cost option?

Could you create a laundry closet (either drywall with doors or built-in cabinetry in the den and put the w/d there?

We just created a small room as part of our garage that also houses the washer and dryer, they were originally there, they are now enclosed with dry wall and a door.
Your den could have such a small room where the connections were to bigin with, and just enclosed it.