What is the difference between N-MORB, E-MORB and OIB?
The nomenclature is confusing and recent studies have shown that among mid-ocean ridge basalts (generally called MORBs) that  normal mid-ocean ridge basalts (NMORB) should reflect the statistically usual composition while enhanced MORB (EMORB) and depleted MORB (DMORB) should reflect end-members of the MORB population.  Gale et. al 2013 proposes the use of the term NMORB to refer to the most likely basalt composition encountered along the global ridge system distant from hotspots. The NMORB is given by the lognormal mean of the compositions of ridge segments more than 500 km away from plumes excluding back-arcs.  Contrary to some literature discussion,  NMORBs are NOT depleted in trace elements according to this Gale's work and so linkage between the idea of depletion and NMORBs should be broken. 

Gale et.al propose the term DMORB to recognize trace element depleted basalts. DMORBs would not be considered representative of the upper mantle or ocean crust nor would they be commonly found in ridge systems.  Finally, EMORB would refers to incompatible trace element enriched NMORBS via a statistical definition found in Gale et. al.  This statistical definition is due to the fact that current data does not allow clear spatial linkage of EMORBs to any particular form of ridge or plume system or island located near to both.  

A good example of an EMORB system is given by Iceland where the rate of magma production has caused volcanism to build the oceanic ridge above sea level.  In this environment, the predominant basalts are also tholeiitic basalts, but there are higher concentrations of incompatible trace elements. EMORBs are enriched in incompatible trace elements such as K, Ba, La, Rb compared to NMORBs.  By incompatible, one means elements that do not fit easily into the crystal structure of mineral elements in the mantle and are usually not found in upper mantle derived rocks because they are preferentially ejected into the melt. 

See this paper The mean composition of ocean ridge basalts - Gale - 2013 for a detailed discussion.

Generally, all MORBs are tholeiitic basalts occurring in oceanic spreading centers, such as an ocean ridge away from hot spots and back-arc basins. At these spreading centers, a relatively small range of chemical compositions of basalts are erupted to form the basaltic layer of the oceanic crust.  The main melting mechanism is likely decompression melting due to rising convection cells moving upward through the mantle beneath the ridges. The composition of these basalts typically ranges from olivine to quartz tholeiites. Tholeiitic magmas are sub-alkaline, meaning they contain less sodium and potassium than other basalts and can be distinguished from other basalts by the redox state of the magma from which they crystallized—- tholeiitic parent magmas are reduced whereas calc-alkaline parent magmas are oxidized.  All three NMORBS, DMORBS, and EMORBS share common chemical compositions (ordered by decreasing wt%) of SiO2, Al2O3, MgO, FeO, CaO.  They also share a common mineralogy of plagioclase, pyroxene and olivine. The plutonic equivalents to a tholeiitic basalt are diorite, gabbro, and anorthosite.

For the next section, this is a great reference!

Oceanic Island Basalts –basalts associated with islands in the ocean basins that generally occur away from plate boundaries, and are often associated with hot spots.  Most oceanic islands appear to be related to ascending plumes of hot mantle which operate independent of the main convection cells that ascend beneath ocean ridges and descend at subduction zones.  A wide variety of rocks occur in these islands, not all are basaltic, but all appear to be related to upper mantle melts.  One may find tholeiites, alkaline basalts, Hawaiites, trachytes and rhyolites in an OIB environment which span the compositional spectrum of magnesium, iron and the alkaline elements. From a melting perspective, low pressure environments tend to produce the tholeiitic magmas and high pressures are required to derive alkali basalts.  OIB mantle sources are enriched in incompatible elements and demonstrate a wider variety fractionization than MORBs. How does this occur?  a recent theory for OIB sources posits that subducted lithosphere sinks to the core/mantle boundary and mixes with the mantle to produce an enriched mantle which heats and rises in narrow plumes which channel this enriched mantle melt upward producing hotspots which produce the compositional variety of OIBs observed.