Moeritherium looks so much like a tapir because they're closely-related members of Order, Perissodactyla, animals with odd-numbered hooves.  The tapir side of the family (Embrithopoda) inherited three-toed feet (on the hind legs), and led to things like the rhinoceras and the titanic Indricathere.  The five-toed side of the family (Tethytheria) split into two major groups, Proboscidea (the elephant family) and Desmostylia, which include sea cows.
Sirenian Evolution
At left is an artists' conception of Moeritherium, one of the most basal members known of the Order, Proboscidea which includes elephants.  On the right is an artist's conception of Pezosiren, one of the most basal members yet known of Order Sirenia, the family of dugongs, "sea cows", and manatees, even though no modern manatee has legs anymore.  .

It turns out there is more than just superficial similarity here.  Jugding by comparing both their skulls and their genes, elephants and manatees have a surprisingly close ancestral relationship.  
"This is the most primitive fossil found so far.  We've found others with legs that couldn't support the animal's body weight. But this is the first whole skeleton with legs that could support the animal's body weight out of water, yet has clear adaptations for aquatic life.  We essentially have every stage now, from a terrestrial animal to one that is fully aquatic."
--Dr. Daryl Domning, paleontologist;
National Geographic News

"Together with fossils of later sirenians elsewhere in the world, these new specimens document one of the most marked examples of morphological evolution in the vertebrate fossil record.” 
--Dr. Daryl Domning, D. P. 2001. 
The earliest known fully quadrapedal sirenian. Nature 413:625-

Pezosiren was in every other respect, a modern manatee, except that it still had a definite, (albeit reduced) pelvis and four still fully-functional legs.  The tail was missing and may have been heavier than indicated here as they evidently used them early on.  Otherwise, Pezosiren must have occupied a similar niche to what hippos do now, spending almost all of its time walking the bottom of shallow waterways -which manatees today still do.
Prorastomus sirenoides
Owen, 1855 (Middle Eocene from Jamaica): 

Reduced sacroiliac articulation, but could probably still support its body weight out of the water. 

Image at right is an artist’s conception
submitted by Daryl P. Domning

Sirenian skulls even today are very similar to Proboscidian skulls, especially basal forms like Moeritherium.  In addition, with Sirenians we have a complete sequence of transitional forms from Prorastomus, (a pre-Sirenian form) to walking manatees like Pezosiren to subsequent forms which still had all four legs, but weren't able to support their bodies out of water anymore.  They had become obligate swimmers.  We then we have others in which the rear limbs are so small as to be impossible to do anything with anymore.  And these lead to a form where the pelvis is gone altogether, and the rear legs have dwindled to no more than a single bone. 
Proboscidian tails dwindled into little more than fly swatters, but Sirenian tails developed broad and and flat like beaver's tails.  This is how manatees' tails still are today.  Dugongs (sea cows) are another member of that family, and they are more derived [evolved] in that their tails have flukes, a much more efficient crescent shape like whales or sharks have.   
With the exception of sea cows, Sirenians are exclusively tropical.  Their fossils are usually found in what used to be the Tethys sea, an ancient ocean that once divided the supercontinents of Laurasia and Gondwana.  Both of these further divided eventually forming the continental masses we have today.  But the Tethys sea is now dry land.

Evolution usually leads to a branching out of several distinct forms, rather than changing just one. That's how evolution theory explains biodiversity and the evident ancestry implied by taxonomy. Sirenians diverged into several different families, some of which are now completely extinct, and known only from fossils.  Sadly, some of these species remain unnamed, and there are no available illustrations of them to show. 
Hooves are essentially just really thick fingernails that cover the whole tip of the finger.  Whales and Sirenians both evolved from separate sets of hooved land mammals, but not from the same families.  Whales are descended from carnivorous artiodactyls, but Sirenians are descended from herbivorous tapir-like things.  The idea that anything could go from hooves to fins may be a difficult one to accept.  But compelling evidence of this is the fact that Sirenians still have hooves.  And there is no other explanation for why anything with flippers should still have finger bones, much less fingernails, and especially not hooves! 

The Systematic Classification of Life