The smallest oozes (Medium and smaller) are easy to represent with just a single brick, or a very simple build. Radar dishes (2x2, 3x3, or 4x4) are good choices here, as are "boat plates." (The latter are 2x2 round plates designed to fit into the bottom of a brick or plate, and are most commonly used to help lock pieces on the bottom of a boat or other flat-bottomed vehicle.)
Giants column about bases and size categories, but keep in mind that when you're building an ooze, the base is usually part of the creature itself. In fact, the very simplest mini for a large ooze is a baseplate of the appropriate size and color.
|8x8 radar dish; 4x4 sphere halves; 8x8 base built from 4x4 plates; and a black pudding built solely from 3x4 minifigure bases|
Some oozes are transparent, which gives these mindless creatures some degree of camouflage. If you own enough transparent bricks, try building your mini with those--or mix them with opaque bricks to expand your options.
A gray ooze is Medium, so a 3x3 or smaller clear or smoky transparent radar dish or boat plate is the most obvious choice. Giant amoebas and slithering trackers (both from Pathfinder Bestiary 2) are both Small, so use 2x2 pieces for them. For the amoeba, you can add a darker colored 1x1 round plate or tile for its nucleus. As discussed in the Tiny Creatures installment, an amoeba swarm can be represented by four identical amoeba minis.
Gelatinous cubes and some other large oozes also have an engulf attack. Building an ooze as a hollow model, using cockpits or other large pieces, allows you to represent an engulf attack by actually placing the victim's minifigure inside the monster.
Ochre jellies, black puddings, and certain other oozes are immune to some forms of damage (usually slashing and one other type), and are instead split into two oozes (each with half the original hit points) whenever they are hit with such an attack. In D&D v.3.5 and Pathfinder, this special ability's text states that the monster splits into "two identical oozes," while D&D Fifth Edition specifies that each new ooze is one size smaller than the original. Both versions specify a minimum hit point threshold below which the ooze no longer splits. 5E also gives a minimum size: Small oozes can no longer split.
As a brief aside, I'm inclined to introduce a house rule into v.3.5 and Pathfinder games to make split oozes one size smaller, as in 5E. Otherwise, you could end up with the nonsensical result of having up to 16* Huge black puddings trying to fit into the same space! (This nearly happened in one adventure I recently played.**) The one drawback to adding this house rule is that it requires changing size modifiers to AC, attacks, and grapple checks on the fly. (5E omits this level of detail, so changing sizes is trivial during play in that edition.) Alternately, you could simply ignore the changes to size modifiers--it's dead easy to hit an ooze at any size, after all--but consider that grapple checks tend to change dramatically between size categories, even when Strength and Base Attack Bonus remain the same.
To return to model building, if you are playing 5E or adopting its rule about split oozes being smaller, then you will need to prepare for that effect on your creatures. You have two choices here: Either replace the ooze miniature with two smaller models, or build your full-size ooze so that it can be broken into smaller pieces. The Large ochre jelly ooze shown below can be broken into four parts, each consisting of a 2x3 plate and a 2x2 plate. If it gets split, disassemble it and use two of these quarters for Medium jellies. If split again, separate the two plates to make Small jellies. Coincidentally, the minimum size of Small lets us sidestep the challenge of fitting multiple Tiny minis into one square.
Even More Oozes?
For the sake of space, I've limited this column to oozes found in the first Monster Manual or Bestiary, plus a couple more from Bestiary 2. But the Pathfinder Bestiary also includes the dreaded shoggoth, which grows eyes, mouths, tentacles and other organs from its bulk. That requires a much more complex model, so I will conclude with some pictures of a mini that combines several techniques for building those limbs and other organs.
* In Pathfinder, a 105 hp black pudding splits into two 52 hp puddings, then 26 hp, then 13 hp, and finally 6 hp, which is too weak to split further. With this house rule, the ooze would stop splitting at 13 hp (Small). A v.3.5 black pudding has slightly more hp (115), but the same number of potential splits.
** The pudding was located at the bottom of a pit, and our failed attempts to hurt it resulted in 8 puddings at one point. The GM (my wife) handwaved the increased space that a stricter interpretation of the rules would have required, and simply used a stack of 3x3 black radar dishes to show us how many were left.
*** Per the D20 Call of Cthulhu RPG.