My sister and I rented a house in Virginia. After we signed the lease for a second year, my sister moved to another state to be closer to her kids. When she moved out, my son asked if he and his girlfriend could move in for a while. They were not on the lease but we made a verbal agreement that they would pay half the rent. They both lived with me for 6 months and then they broke up and she moved out. My son agreed he would continue to pay half of the rent but it has been 4 months and he has not paid what was agreed upon. I want my son out of the house! He is not on the lease. My questions are: 1) Can I evict my son or do I need the landlord to evict him? 2) If I can evict him how long of a notice do I need to give? 3) Do I have to evict for failure to pay rent or can I evict him because I don't want him living with me anymore?

You are his landlord, so you evict him. You would and can evict him for non payment of rent,
You start by giving him a pay or quit notice, ( of course he could merely pay the rent due)

... My questions are: 1) Can I evict my son or do I need the landlord to evict him? 2) If I can evict him how long of a notice do I need to give? 3) Do I have to evict for failure to pay rent or can I evict him because I don't want him living with me anymore?

1) He was a sub-tenant. Thus you would be the one to evict him.

2) I'd have to look it up in Virginia, but many states allow you to sue for eviction if you have given someone late in paying rent a 3-day pay-or-quit notice.

3) You could evict for both reasons, but you should realize the former reason often has a shorter notice period. If you only evict because you no longer want a tenant-at-will, you have to give something like 30 days notice.