OBV is accumulated volume signed by direction: the volume of up candles is added, of down candles subtracted. A divergence on it is built exactly as on an oscillator, but the quantity compared is different — not the speed of the move but the volume it ran on.
How it differs from an oscillator mismatch
RSI and the MACD histogram are computed from prices. They describe how price itself changed and know nothing about how much was traded meanwhile.
OBV is computed from prices and volume together. So a mismatch on it answers a different question: was the new price high set on more accumulated volume or on less.
Hence the difference in reading. An oscillator mismatch says the impulse is weaker than the previous one. An OBV mismatch says the move is less well backed by turnover.
The starting point does not matter
OBV is a cumulative quantity, and its absolute level depends on which bar you started counting from. The value on its own therefore means nothing.
For divergence that is irrelevant: what gets compared is the difference between two points, and differences do not depend on the origin. There is no sense in looking at "the level of OBV"; there is sense in looking at how it changed between extremes.
When volume cannot be trusted
This is the main caveat, and it is more serious than it looks.
Volume is not as reliable a quantity as price. On many instruments it is aggregated from several venues rather than one; on forex there is no exchange volume at all, and tick volume — the number of price changes, not trades — is usually substituted. There are also stretches where volume was simply not recorded and zeros stand in its place.
If the data has gaps or zeros, OBV accumulates garbage, and a mismatch on it will be an artefact of the data rather than an observation about the market. Before reading a volume divergence, make sure volume on that instrument means anything at all.
A common mistake
Treating a volume divergence as weightier than an oscillator one: "this is volume, and volume does not lie." It does — exactly as much as the volume data itself is unreliable.
The second mistake is adding mismatches on different indicators together as mutual confirmation. They are computed from the same prices and so are not independent; two coinciding mismatches are more often one observation counted twice.