I’m going to sell this property soon as my HOA won’t allow me to transfer it over to an LLC.We want to purchase 5-15 doors (2-6 multi family homes) in the next twelve months and I currently have about $5000 saved and potentially have access to an additional $150k in family/friends money.

They're likely hoping you won't file eviction so they can save up enough of the money they are not paying you to find another place. 

The problem is that our credit scores and savings are low.

If I could save up $5000 by graduation do you think it’d be smart/possible for me to get a loan on a house?

Nobody replaces a functioning AC just because they've saved up. 

-Stay at home and save for another 12-15 months-Use FHA financing to buy a first multifamily property (2-4 units)-Live in one unit while renting out the rest-Pay down mortgage for 1-3 years, refinance FHA status into a conventional loan-Apply for another FHA loan and repeat the same process in another propertyObviously it would be better to buy and find a property that can cash flow.

@Tim White sounds like you may have to get a higher efficiency washer and dryer and do the Laundry onsite to save time.

IKI'm 23 yo and I've been saving and saving and working/working to try and save enough to qualify for an FHA in order to purchase a home. 

Save every dime you get.

I recently moved graduated from college, started a decently well paying job, and moved back home to save money for the next year or so.