What injuries can a 7 week old baby sustain from falling off the sofa?

Usually none. Because babies are resilient and it is a short distance. If the floor is tile or un-carpeted it is possible to sustain a broken arm or skull fracture or scratches or cuts it they hit something on the way down. If your child fell and you are worried, call your pediatrician.
Head injuries. Although most babies will not have a serious injury, there is always a possibility of a head injury from any fall. Never leave a baby on any unattended surface- the sofa, a bed, the changing table. A good rule is to always have one hand on the baby at all times, unless she is secure in a crib, playpen, infant carrier or other safe environment. Prevention is the key!
Infant falls. In part it depends on what the surface is when the child falls. If it is wood or tile, there is a great chance that the child can be seriously injured. Infants are top heavy and tend to fall on their heads. You should have the child checked by your pediatrician. If the surface is carpeted and it is a soft surface, there is less chance of being hurt. You should never leave an infant unattended.
Difficult question. This depends where the baby fell, the surface, what they hit, and how high the couch is. A 7 week old could do damage to any area in their body if they fall wrong, or they could be fine, but the most concerning thing is their head. If they land head first, this would be the most worrisome thing and a visit to your doc would be recommended if you had any concerns at all. I hope this answer help.