Traditionally, moving is a time to find out who your true friends are. For a very small move, you may need nothing more than a friend with a truck (and some cash to treat your friend to food and drink!).
If someone wants to help, but is not physically up to helping you move boxes, he or she might be able to care for your kids or pets on moving day, or help with cleaning your old place.
If hiring movers is too expensive, you may be able to hire helpers to load and unload a rented truck that you drive yourself.
Consider low-cost options -- a friend's house? camping? -- to save on lodging during the move. Plan and pack a cooler of healthy picnic food to save money and care for your family's nutritional needs in transit.