I have three toilets in my newer, 3-year-old residence; the toilets will surge throughout the day and night, sometimes several times a minute and may last seconds at a time; I take the cover off the tank and notice the water level is rising. My water bill has increased substantially, and I worry there may be leak in a pipe somewhere in the residence that I can't find. What do you suggest?

Tell what you mean by surging. Sounds like you are saying that your toilet tanks are leaking and periodically the fill valve opens and refills the tank.
If that is correct the flush valve (flapper ) is leaking and needs to be replaced.

All three toilets?

Possibly. Same brand of toilets, same brand of flapper. Flappers all deteriorated at same rate. Could also be chain to flush lever to tight.
Could be one toilet leaking but hearing it through out the house.
Could be something else, all depends on what surging means.

Harold, I was directing the question to the OP.

This could also be an indication of water pressure issues. Are you connected to a municipal water source? If so, and if you have a standard water pressure regulator at the entrance to your home it may have failed.(pressure too high)