We are using CISCO 3750 series switches( total 3 WS-C3750X-48P). Can we use "Cisco StackWise Plus Technology" to connect all three switches considering that the 3rd switch is located at around 150m from the other two switch?
If you have the budget, yes get a switch to provide distro/core function and uplink all the 3750s to it. If not, you can daisy chain the 3750s together.
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What option do I have to interconnect the 3 switches? Do I need core/distributio to connect them?
One option would be to use fiber. You'll need one of the SPF option modules for the 3750-Xs. Don't need core/distribution but if you have that already, and it's within copper distance, that would be another option.
BTW, the 3rd switch would not be part of the stack when unable to use the stack cables.