What would happen if a Cessna flew into a power line?
There are a lot of variables so its hard to make a flat out call. Here is at least one example of it happening that was caught on film. In that instance it seems to have ripped through the cords (which also appears to have started a fire). However here is an example of a similar situation where the plane simply got tangled into the cables and hung there. This one from my home field (ill go do some more digging) but it looks like the cable ripped it apart. 

I would say you have a few mitigating factors, 


Is the engine running? the prop is sure to do some slicing on impact if your engine is running and your prop is turning. 
The cable type. As Ron mentions in the comments the type of cable will have an effect on this. The higher voltage cables tend to be solid twisted cable securely affixed to the larger towers. While the stuff out side your house is of a much smaller gauge and possibly is a phone line or other coax line etc.  
Speed and size. There are lots of aircrafts that are all capable of very different types of flights. A Mooney Mite on departure is going to impact a power line in a far different manner than a King Air on departure. Its simply a matter of inertia.  
Insulation Joints. Power lines are generally connected to towers via some kind of insulated connector. Often times the connectors used can break away under enough force allowing the line to drop to the ground. This of course depends on the type of connection joint and direction of force applied.