Sure, is possible.
Supply power to each string from 12V or whatever source they need.
Use an NPN transistor, such as 2N2222, to control the ground of each strip.
The arduino then controls the transistor.
You need a 150 ohm resistor between arduino and transistor base.
Transistor emitter goes to ground.
Transistor collector goes to the "negative" of the LED string.
"Positive" of the string goes to +12V or whatever power source it needs.
May need a current limit resistor in series with the LED String, or it may be built in.