To communicate Origin with individual instance of Mathematica directly, you must configure Mathematica to run Origin's kernel OSequencer.exe. Otherwise Origin can only communicate with a Mathematica kernel that is launched when the Mathematica Link tool is invoked. If you don't need to communicate between Origin and a Mathematica instance that is launched, please ignore the first part of configuration inside Mathematica.
Once done, you can go to folder C:\Users\<username>\AppData\Local\Temp and open the OMAthLinkConfig.INI file.
Location=C:\Program Files\Wolfram Research\Mathematica\<MathVersion>\MathKernel.exe
Check if the path points to the correct Mathematica installation folder with which you want Origin to communicate. It is especially important when you have more than one version of Mathematica installed. If not the correct path, you can: