Electrical power lines can attract and repel each other, but the amount of force involved is incredibly small under most common conditions. Current in two wires flowing in the same direction attract each other, and currents in opposite directions repel. The magnitude of this force over a wire of length L (assuming the currents in each wire are equal) is

F=mu*I²*L/(2*pi*d) where:

-mu is called the permeability of free space (1.26*10^-6 Newtons/Amp²)
-I is the current in the two wires
-L is the length of the wire (meters)
-d is the distance between the wires (meters)
-F is the resulting force in Newtons, which can be converted to pounds of force by multiplying by 0.225.

To take an example typical of a high power kitchen appliance like a water kettle, the current in the two wires going to the outlet in the wall is about 10A, and the distance between them is about 5mm. Over a 1 meter wire length the force is only 0.004 Newtons, which is a bit under one thousandth of a pound, so it's very small!

So you can see that for pretty much any case in day to day life electrical wires will attract and repel each other, but it will be unnoticeable because it is so small. One case where these forces matter is in high-powered electromagnets, like the superconducting electromagnets in MRI machines. There the current is high enough that the force is noticeable, and the coil of wire has to be reinforced so that it can hold its shape.

When a current runs through a wire, the net movement of charge disturbs what we call the electromagnetic field. We call this disturbance a magnetic field and the attraction you are referring to is generally between two wires with direct current moving in the same direction creating magnetic fields that interact with each other to force the two wires closer together. The power lines we use to 'send' electricity to our homes is actually alternating current, not direct current, so if you think about the equivalent magnet it's always changing direction. This rapid change in the orientation of the magnetic field caused by an AC current doesn't impart a constant attractive force. In addition, electric lines are far enough apart and insulated that different lines don't interact at all.

I should mention that the nature of these forces and how to understand them is really something you need to tackle in a classroom and over a long time. Ideas like these are highly phenomenological right now and there is rarely a simple "just think of it like a bar magnetic" explanation (it pained me to say 'equivalent magnet' above). Our best fundamental understanding of how this happens is through Quantum Electrodynamics, but the answer to your question is at least on some level embedded in the paragraph above.