You have received a lot of good suggestions on how to get rid of them. It's true that you need a 2-pronged solution (fleas, and then the remaining eggs). As for the source - there is a bumper crop of acorns this year and so squirrels are frantically gathering them. One may have worked his way into your basement - it's pretty easy. Same with chipmunks. The other source is a field mouse - they are unbelievable at flattening their bodies and entering a house along a joist or along a pipe - like where the water goes out from the basement to the outdoor spigot. As the nights cool down, animals may get in the basement looking for a warm place to build a nest for the winter. The fleas are happy with any warm-blooded host, and they are good at jumping onto a cat or a human. For the squirrels, look for a hole anywhere about 1.5 inches across. For the mice, forget it - you can't mouse-proof the house, only get rid of the ones you have.
You can try the natural solutions mentioned or consult an exterminator who uses environmentally-friendly (and child-friendly) solutions. Sometimes the exterminators can spot the source of the problem by identifying entrance holes, small amounts of damage you can't spot, or droppings. But definitely do something!