The Mole called by the Saxons 'the ploughman' is useful in poorly drained soil as it aids the flow of water. It removes all forms of soil pests from grubs to beetles.. Sadly they also eat worms. The main reason for killing this poor little chap seems to be it adds interest to an other wise manotanous green lawn.
If you insist on killing this friendly little chap try;
A stick of dynamite in the tunnel, This will send a compression wave down the tunnel, collapsing the moles lungs. It is full-prof and by filling the resulting hole with water you will gain an attractive feature.
The fox, they will control moles by eating them. Another reason to leave the berated fox to thrive, but the holes will be bigger where the fox has had dinner.
Then there is the cat solution. To stop moles coming into your garden buy your own mole. This mole will keep others out.
Depends on what size garden and the surrounding green you have. Vibrations are usually the best deterrant as previously stated. Some also have slight electric shocks while others prefer to attempt to place metal sheeting all around the border of your garden.
Moles are very territoral, and are often found alone. Its really only the nake mole rat found in africa that huddle together. The Townsend Mole (dig the most and cover the largest area) are the hardest to control.
Best of luck with your new found friends.
Mole.
Have you ever had the miss-fortune to have party folk next door. Take my word for this. Set up a party, loud music, Pynk Floyd is good. The moles will soon put up a for sale board, and move out.