1. "I have an interview tomorrow." That's good!
2. "I am going through an interview tomorrow." No. However you could say: "I am going through part of the interview process tomorrow." This would apply if there were more than one step to the process.
3. That one is perfectly okay.
4. "I needed to go through an interview to be accepted in this position." Almost, but not quite right. "I needed to go through the interview process to be accepted for the position." However, I'd prefer: "To be accepted for the position, I had to go through several interviews." or "To be accepted for the position, I had to be interviewed."
Hope this helps!