After making sure all waste water is drained first, I always use a length of old stair carpet -- usually about 3 times the size of the washer. Say if the washing machine is 30 inch deep (front to back), then cut a length of old staircase carpet 90 inches long.
To get the washer out of the house and into the vehicle:
Lay the carpet piece out on the floor from the front of the machine with the carpet pointing in the direction you intend to go, with pattern face down, and gently lower the machine onto its side at the back end of the carpet, with the feet at the rear, leaving a few inches of carpet sticking out at the rear. If it is a front loader make sure the machine door hinge is at the top of the machine door (once you have it on its side that is) and the catch/latch is at the bottom -- that way, the washer door won't come open due to it hanging down from the hinge.
Pick up and grip the long free end of the carpet firmly and drag the carpet with your back facing the direction required and it should just glide across the floor with the machine as a sort of genie on a magic carpet. No expensive dolly or hand/sack truck to buy -- just an old length of carpet.
If there is a threshold across the doorway on the floor, keep pulling the carpet over the threshold until the washer is able to rock like a seesaw over it, then apply a bit of left pull of the carpet and then a bit of right pull, and left, right, left, right, only inching along bit by bit until the very bottom/back end of your cargo has only a little lip left to go, and stop. If the threshold is too high to risk allowing the machine to plop over the obstacle by your magic carpet trick, then have a few bits of wood or even a rolled up old bit of carpet to act as a sort of cushion on the ground (nearest to the outside of the threshold), and just ease the magic carpet, with the machine still in position on the carpet, and ease the load outside with the small left pull, right pull, bit-by-bit method and away you go. I can assure you that whereever you pull the old carpet to, the washing machine will follow.
Hopefully the transport/car or van will not have a floor height higher than the top of the washer when it is stood upright. Place something like a bath towel over the vehicle threshold to avoid scrapes or scratches to either washing machine or vehicle. Now your muscles get a workout. But always please slowly, slowly, position the now uprighted washer with its least sticking out bits facing the
vehicle and at a bit of a distance from the vehicle (about two thirds the height of the machine) so that when you tilt/lean the washing machine towards the transport, only about 3 or 4 inches sit on the vehicle threshold. The washer should be positioned at such a tilt that it sits there already inside of the vehicle at about 45 degrees on its own with about 3 to 5 inches -- possibly more but not less than 3 inches.
If you feel that its a big ask to lift and push the washer at the same time, have a milk crate or sturdy wooden box of a height that you feel you can lift up t, then you can do it in steps. Always lift with knees bent, back straight. Have the box handy so that you can kick/slide the box with your foot twixt ground and washer. Then you can lower your heavy end onto the box whilst the washer's other end sits there until you get your heavy end to a height where you can slide the washer into the vehicle (another seesaw on the vehicle's lip twixt inside and outside). You can lift the washer in increments of only a couple of inches at a time as long as you have a box/wooden block for each 2 or more inches of lift. But watch it, don't let the washer push you backwards, don't rush, and it's best not to bend right down to lift the washer by the feet nearest/sat on the ground -- just lift from what should be the uppermost edge, approximately a couple of inches below your waist height. Lift and push at the same time for the last couple of inches, and once the balance occurs (seesaw), tilt your end (with your finger) and the washer will slide almost all the way into the vehicle.
Once it is sitting in the vehicle with its feet sticking out, climb inside and pull, remembering that you need to soft-fill any drop inside, so that the end that you lifted up doesn't have to drop too far when pulled from the other end.
Sorry it was a bit long winded but I move a heck of a lot of domestic appliances and I never go on a job without my magic carpet, which polishes wooden floors a treat if you place the piece of carpet pattern face down. I could have just said stick the washer on an old carpet and drag the bugger out.
But there you go, it works a treat every time, and to be honest this method is not exactly a strain like most folk seem to think. Slowly, slowly and a bit of balancing (seesaw effect). I am only about 5' 5" and 140 pounds in wet clothes and I wouldn't use any other method, because it doesn't cost me a penny. The only "equipment" I need is an old carpet and some milk crates or wooden crates or anything that will act as a place for the washer to sit on in increments of a couple of inches per lift.
See ya, hope it helps, all my best wishes, Kenny, Padiham, Lancashire, England