Level Switch

Any wire that can withstand relay coil current will do the job, however any statutory or regulatory requirement can super-seed my statement.

connect the NO, NC, Common terminals in level switch to the motor (load).

Any conductor capable of carrying the amperage of the load and conforming to local regs and process environment. Also, I wouldn't operate the motor directly from the relay contacts but rather use them to operate another control device such as a motor contactor.

yes sir, you are wright. I am going to activate motor contactor through level switch. The contacor rating is 24 V dc. Shall I use twisted pair signal cable, what we use for analog signals (4-20 mA).?

Follow the advice above.

Twisted pair would do it, though it is unneccessarily highly specified for an extra-low-voltage relay switching application. If it is the only cable to hand then so be it.