Lenders are saying our income is too low.

You can get a loan for slightly cheaper depending on your credit score and LTV that you are looking for Ive seen as low as the high 5's to mid 6's on the interest rate 

You can try to justify a low offer all you want, but chances are somebody else will come by and pay what they are asking. 

I am considering making offers at what could be considered low ball prices (30-50K below listed price).

I can absorb the worst case scenario for one ARM since everything else I hold is on low fixed rates and cash flows well, but I'd be wary of collecting a bunch of ARMs like this if they all have the potential to go negative cash flow.

If you live in a low cost area in the United States this can become easier to accomplish versus an expensive part of the US like CA or NYC where you're going to need a lot of cash flow to meet your goals.    

Make sure there is no or low interest.

I'm trying to buy a 4 plex, and live in one of the units.The problem is that the rents are currently too low for the apartments to cash flow with all four units, and the rents would just barely cover the mortgage if I lived in one of the units.I could live there practically for free but what would I do when I wanted to move?

Prices are high, expenses are high, and rents are modest so the strategies that can get you enough to live on, to give some examples, might be student housing, higher risk cities with low house prices and poor economic fundamentals, or starting with buying a multi-million dollar portfolio requiring hundreds of thousands or a million+ of down payment. 

How low of a credit score should I accept?