You can use System.Diagnostics.Process to execute an .EXE, and can even capture the output if it is a console / command-line application.
You would have something like this (but bear in mind this is simplified quite a bit!):
dim process as System.Diagnostics.Process
process.StartInfo.FileName = "program.exe" ' You need to be smarter here!
process.StartInfo.Arguments = "whatever command line options you need"
process.Start()
To check if the program is still running you call
process.HasExited()
If you want to capture the output you need to set StartInfo.RedirectStandardOutput to True.