Hi @Antonio Evans,
Every situation is different so this may be something you want to discuss with a tax accountant. I'm not sure the reasons for you taking over the payments. Is it to help them out or for the house to transfer to you? What are your plans for the house?
I looked into to doing this with my dad's rental in VA but it ended up not making sense. Since he has used the house for a rental for multiple years, he can no longer take depreciation. If I put myself on the title now, then I won't be able to take depreciation. However, if I wait and the property is transferred to me upon his death, it is transferred at the market rate. So then, if I use it as a rental, I will be able to take depreciation. That is a big deal for me.
I'm not sure where the townhouse is in VA but many markets are very hot so now may be a good time to refinance. It is typical that the winter does slow down a bit though. One idea about the appraisal would be to pull comps for the area. Why do you want to refinance? You could also just pay their payment and keep the loan in their names.
So many options...