Removing the process should be pretty easy: change the security on the EXE to deny the Execute permission (this can be done on a file with running processes), and then run taskkill /f /im Wslxrqjet.exe to terminate all instances of the running process as simultaneously as possible. New instances won't be able to start (unless something reset the permissions on the file). You can then delete the EXE.
Another option would be to create a new user with admin rights, log out of your account, log into the other user, and delete the file out of your usual account. You could also shut down and boot the machine off different media (such as a Linux live image on Windows install/recovery disk), mount the C: drive, and delete the file from there. There are lots of ways to handle this.
You can also try investigating the process while it's running. See which process launched each instance, who it's running as, and more by using a tool like Process Explorer (free download, part of Microsoft's Sysinternals suite). See what the process is doing by checking its network activity, file handles, and so on using Resource Monitor (built into Windows, gives more details than Task Manager) or - for tons of detail - Process Monitor (also free, part of Sysinternals). Even if it is malicious - not guaranteed - it's had long enough to run that it's probably done it's harm at this point. However, if you want to prevent it from doing anything while you examine it, use Resource Monitor or Process Explorer to "Suspend" the processes.
