Here's the situation. Tenant that is on the lease goes to jail late January. Friend had been staying there since November paying a little rent but not on the lease. This friend doesn't pay the rent for February. Friend goes to real estate company and informs them of such. The real estate company decides to let her apply to be on the lease with his permission. The note was forged.
Anyhow, this friend calls my boyfriend and I asking us if we wanted to go in on it due to the steep and this place is just perfect for what we were looking for and we need to move out soon. It turns out the friend told the real estate company we agreed to pay all the back charges plus current charges totalling $3600. This was untrue of course, as we had just paid our own rent for those two months where we dwelled.
This friend will not pay and will not give the keys up to the real estate company.

WHAT IS THE Most quick WAY TO EVICT BOTH OF THESE PEOPLE SO THAT WE CAN TAKE OVER ON THE LEASE AND PREVENTING FURTHER MONEY LOSS ON THE REAL ESTATES COMPANY'S END?

We are willing to take the house as is!

There's nothing you can do, you aren't the landlord or the management company. If you didn't sign anything saying you would take over this $3600 lease you can wait it out and see if the guys get evicted for non-payment, or you can contact the management company yourself and explain your interest should the place open up. But really, that's about it - you have no authority over who lives there since you are not an owner or agent.

You could also give up on this place and see what else the management company has available to you.

There is as noted nothing you can do to evict these people. The owner or the management company has to evict them.