Full Tilt Poker, $0.25/0.50 Omaha Cash Games, 6 Players
Board:
UTG: $50
UTG+1: $91.80
CO: $52.75
Button: $92.30
SB: $50
Hero: $73.05
Dealt to Hero
Pre-flop:
(2 folds), Button calls $.50, SB calls $.25, Hero raises to $2, Button calls $1.50, SB calls $1.50

Flop: ($6.50) (3 Players)
SB checks, Hero bets $6, Button calls $6, (1 folds)

Turn: ($18.50) (2 Players)
Hero bets $15.50, Button calls $15.50

River: ($49.50) (2 Players)

On the river I see that we have three different options: Bet/Folding, Bet/Calling or Shoving.

Bet/Folding and Bet/Calling

The decision whether to bet/fold or bet/call for a small amount ($10-20) is largely opponent dependent. If we feel that the villain in this particular instance is quite loose-passive (In this particular hand this is hinted at by the fact that he limp/called the button.), then bet/folding is not an entirely poor option since it’s quite unlikely that he will raise us with anything less than a set or straight and we’re losing often enough to make folding ok.

However, if Villain isn’t overly passive, and is capable of shoving over the top of us on the river with his missed flush draws and all of his two pair hands, then bet/calling the river becomes a viable option. The reasoning behind this is that an aggressive player is much more likely to raise on the turn with this set hands, and most hands that may have made a straight would most likely have been folded on the turn. Of course it is quite possible that Villain could display a set or straight here, but there are much more two pair combinations in their range which makes bet/calling profitable if he is capable of raising the river as a bluff.

Shoving

Shoving the river is also quite a good option. After Villain floats the flop/turn, his most likely holdings are flush draws (with or without a pair), two pairs, one pairs, sets, 89T.
Sets and two pairs are less likely combinations within this range, since they are fairly likely to raise you on the turn thinking that it’s quite possible that you yourself are on a flush draw. One pair holdings and 89T quite often fold the turn, and are a fairly small part of the range on the river.

From Villain’s perspective, the on the river did very little to our hand, and he most likely puts us on a AAxx or KKxx type hands, a flush draw, or a Jack with high cards. Since we bet out of the blinds, AAxx and KKxx are the hands out of these that Villain will most likely be putting us on. Because of this, shoving the river becomes quite a good option as they are fairly likely to look us up with most, if not all, of their likely two pair combinations which we are beating.