OHCs are Oversized Hardcovers. They're more prevalent with modern titles/comics than with older reprint material. They are the the same dimensions of omnibuses (large than regular premier hardcovers) but usually only contain 11-13 issues (so less than an omnibus, but more than a 6 issue TPB or Marvel Premier Hardcover, which are both also smaller dimensions than Omnibuses or Hardcovers).
For example the New Avengers Omnibus has Avengers 500-503, Avengers Finale, New Avengers 1-31, Annual 1; New Avengers Most Wanted Files; New Avengers : Custom 676: Army & Air Force; Giant -Size Spider -Woman 1; New Avengers: Illuminati (2006) 1; Civil War: The Confession 1; Civil War: The Initiative 1
Which content-wise is the same as having the Oversized Hardcovers of: Avengers Dis-Assembled, New Avengers hardcovers Vol 1-3 and Civil War:Avengers.
In my scenario you can buy the 5 OHCs for less than the cost of the New Avengers Omnibus. (this isnt true in this case but it was the the simplest HCs aligning to an Omnibus where there are OHCs available). So why buy the Omnibus? Its bigger, bulkier, harder to read, and costs more!