1.   Fresh water - always seems to be in short supply at the site of any of these disasters.  The Oilers could easily be configured to carry a million gallons or more of potable water. Also need some new technology desalinization plants to make more water.  The retired oiler evaporators can hardly keep up with her own steam leaks. 
    2.   Cargo types:  adding side doors and converting the formerly liquid cargo tanks into a sort of "RO-RO" support ship.  This requires a lot of expensive design and engineering, but it is do-able. Designers might also look at deck cargo (coastal disaster relief typically requires building materials, small boats, landing barges, trucks, ambulances, etc. etc. that would constitute deck cargo).  But the Oiler's are not strong on handling deck cargo.  The winches take up most of the deck space.  Might want to "clear the decks" and start over with just a couple of moderate-to-heavy lift cranes.
    3.   Airlift support.  When clearing the decks the designer might want to make a big helopad either way forward or way aft - but then there is the problem of getting cargo to those pads.

The big limiting factor I see, however, is the basic steam propulsion plant.  The Oiler's were never "turn key" plants.  They are cranky and high maintenance.  The likelihood of going from extended "cold iron" to underway would be weeks, not days or hours.  They are also manpower intense and incredible fuel hogs.  Even inport steaming consumes a tremendous amount of fuel.  They only way that these hulls could be dependable and economical "start and go" ships would be to convert to low speed diesel w/ huge hotel service diesel electric generators as well. 

So. . . even assuming that the hulls are still sound, the engineering and design expense for converting to some sort of RO-RO, plus deck modifications, plus fresh water modifications plus complete repowering.  The concept of spending hundreds of millions on hardware that would then "just sit there" until needed for humanitarian relief might be a hard sell.  Just look at the "Mercy Ships", a christian medical mission organization that currently has two ships (one still being fitted out).  "www.mercyships.org".  There ships are in use 24/7/365 and still very difficult to support.

The US Navy (MSC) bought seven Sea Land shipping "SL-7" container ships back in the late 1970's.  These ships were practically brand new "super high speed" container ships designed to make regular runs between the US Atlantic coast and Europe at 30+ knots.  They were powered by huge steam turbines (100,000+ HP).  They started to enter service about the time of the 1973 oil embargo.  When oil prices went through the roof these ships stopped sailing because of high operating costs.  The navy bought them for a song and turned them into "RO-RO" ships for the pre positioned force.  They were huge (almost 1,000 feet long) , fast and cheap.  These seven ships could deliver more cargo from the US to the Persian Gulf in 11 days than all the airlift in the free world could deliver in 64 days.  Their operating cost was not a factor because the US Department of Defense was footing the bill.  They have truly earned their keep and proved the concept during both gulf wars.  They are tremendous.