Is there any way to to turn aircraft left or right without using rudders??

yes u can use the engine thrust present on the both side of the wing unequally to provide a movement of the aircraft to turn towards the left . just  increase the  throttle valve  of the right engine more compared to the left engine . but  this will also result in the right engine having more lift resulting in a rolling moment to the left which should be counteracted by the use of ailerons 

We can use ailerons for turning left and right followed with roll.

Second method is with the use of alevons.

yes with the help of ailerons we can turn aircraft .in comercial aviation we mostly use  ailerons for turning

There are different ways to turn left or right using spoilers, flaps, aileron thrust (multi aircraft engine) and elevator.

yup, you can use ailerons to do side sliding

Eelevators ,Ailerons and rudder provides primary movement around the axes of flight.

Rudder is used most often in anticipation of known requirments from the other controls and rudder induce rolls as well as yaw motion of the aircraft.

In a turn,power will make the left turn possible with little rudder or no rudder but required rudder to lead the right turn.

I applogies for being so late to answer the question. Thank you.