How can I replace the outlets when the boxes are too small?
Let me guess: the wall boxes are metal and the "ears" on the new receptacles are hitting the wall around the boxes, right?

The "ears" are scored to allow them to be broken off leaving small tabs with holes in them for the screws into the boxes. Just grip the ears with pliers and bend back and forth. In some designs the ends of the center tabs are  also scored for breaking off to allow fitting into the tightest space.

The ears have holes in them to allow them to be used as shim spacers to stand the receptacle out if the box is too far into the wall. The use of metal shims makes electrical contact of the ground of the receptacle with a metal box. Some receptacles have a paper "keeper" on one of the mounting screws and a metal keeper on the other end. This provides metal to metal contact on the end with the metal keeper. If you are using cheaper receptacles with paper keepers on both ends, remove at least one of the paper keepers to insure metal to metal "face" contact for the ground.

But you would be advised to use a better grade of receptacle. And I assume you are using the now code required "tamper resistant" receptacles, right?

Does your home have aluminum wires or copper wires?