Fluid dynamics is one of those super hard things to set up, that once you've got it working allows for a whole range of interesting effects. It's probably overkill for most games, unless you actually need things to move like a fluid (as in, flow from one point to another). For soft-body masses, I would considering instead using nets of springs to simulate your bodies; much more straightforward to implement, and far easier to handle from a gameplay point of view.
As a possible initial implementation: imagine that your body would have a centroid, that you could apply forces to and move around. Around that centroid, you'd attach additional nodes, linked to the centroid with a spring, and linked to each other to form a network that holds its shape. For example a hexagon of 6 nodes around the outside, each linked to their neighbour and also the centroid via springs. As you apply forces to the centroid, the springs act to pass on that force to the outer parts of the body; the front compresses towards the centroid, the rear elongates as it is pulled with the centroid. That's not the only way to do it, you can have the movement forces applied equally to all the nodes, it all depends on how you imagine these bodies to work internally. Apply forces to all nodes equally, and the body won't deform unless it encounters something else.
And it's in encountering "something else" that things get interesting, and cause your body to deform nicely. Bear in mind you're simulating something soft and squishy, not a bunch of hard spheres connected together. So maybe instead of using rigid body collision, give each of the nodes a repulsion from the other objects in your simulation. Then, as you move your body towards an object smaller than itself, the gap between nodes will widen to allow the object to slip between them. After the object has passed through, the springs that hold the body together will cause it to reform into its original shape. Objects larger than the body won't be able to fit through the gaps, so your body should collide with the larger object and flatten against it. It's possible you want to implement rigid body physics as well, to prevent a squishy object penetrating through something that should be solid, but it should be a backup to the repulsion-based forces that are simulating the squishy exterior of your body.
In terms of rendering, you can get a nice blobby effect with a pixel shader or render-to-texture approach, basically rendering a circle around each node such that the overlaps are invisible, but around the edges there are nice soft circular edges.
So look up spring networks and Verlet integrated spring simulations, and you should be able to get the foundations of a system that will let you do 'blobby' physical mechanics without doing full on free-moving fluid simulations.