Are you under contract to purchase the 4-plex with tenants in place (rather than making your offer contingent upon the units being delivered vacant)? 

Plus they deliver as I do not have the means to pickup.

There have been multiple attempts made to deliver certified mail but never successfully delivered.

If you have texts saying they are going to sign it, and you delivered it some judges/courts will consider that a lease even though it isn't signed as well. 

If it's a good area, meaning high cash flow, it attracts both landlords and tenants, and the quantity of tenants willing to pay high enough rents to deliver the higher CF, is what makes it a good area to invest.

My question is what ability we have to enforce certain “policies” such as requirement to maintain renter’s insurance(their leases don’t require it) prescribed method of payment (they currently deliver cash to the landlord’s local bank) or increasing their deposit (some are as low as $100, and one tenant has no deposit at all)?

You need to make sure that your expectations of a turnkey property are exactly what is delivered.  

If they are together then you need to figure how you work with the two rentals to pay the water bill or pay it yourself.4) You will need to work out how mail is delivered for two parties at one address. 

pid=1803Per HAR, "Along with the first notable cold front of the fall season, October delivered the inevitable to a hot Houston real estate market: cooling sales.

This was acquired as part of a larger commercial package and the property was delivered vacant and in broomswept condition.