Like YEKCIM said, the Olympus is a true DSLR, but it does have a smaller sensor. Here's a graphical illustration of its size:
The Olympus uses a "Four Thirds" sensor, which is about 225mm square, versus the APS-sized sensors found in most other DSLRs, which are about 369mm square. This accounts for them having more noise at higher ISO. There are also other quirks, like a small, dim viewfinder (to accomodate "live LCD" functionality), and mysteriously, not true focus rings but ones that you twist slightly one way or the other and hold while it focuses, not unlike hitting a button on a PnS. You'll also find a smaller selection of lenses and higher prices for the ones there are. On the up side, it
is a DSLR and the lenses seem to generally be very good.
Oh, and the sensor produces images in a 4:3 format like a PnS camera, not the 3:2 format that you find in most DSLRs (and 35mm cameras.)
The Sony H5 uses the little 1/2.5" sensor (as does the Canon S3). The Fuji has a 1/1.6" sensor, which is a good bit larger, slightly larger than the 1/1.8" sensor in the above illustration.
To sum up:
The Sony is a PnS with a big zoom range.
The Fuji is more like a true SLR, with a zoom ring but no interchangable lenses and still a much smaller sensor, but still larger than the Sony's
The Olympus is a DSLR
Also like YEKCIM said, I would definitely consider the Pentax K110D/K100D strongly if you are thinking about the Olympus. Frankly, at the risk of ruffling any Olympus DSLR owner's feathers, the Olympus would the last of the current crop of DSLRs that I'd consider. (I'd go Pentax, Nikon, Canon, Sony, then Olympus. And quite frankly, I'm not that hot on any of the currently-sold entry-level Nikons or Canons, I'd have to go to the next models up in each system. If you can still find a Nikon D50, I would give that consideration, though.)
If you were sticking to those three you listed, though, I'd probably lean towards the Fuji, even though it's a lot of money for a camera that still
isn't a DSLR.