Okay, I tried resisting posting... but I'm going to give a shot at answering because I didn't agree with a lot of the answers. So, instead, I'm going to answer by proposing thought experiments.
T.E. #1: Vessel of water in space
Imaging you're aboard the ISS. You've got a cylinder filled with water that is plugged on one end. The other end has a plunger that's loosely containing the water.
What happens when you press down on the plunger?
Well, the pressure in the water builds - you're putting pressure on it. But, generally, the water is staying the same volume - because water is pretty darned uncompressable. Water at the bottom of the ocean only manages to compress water 5%.
And if you press really really really super-humanly hard? Then the water actually condenses to a solid. Which really doesn't compress well.
T.E. #2: Filling ISS with Water
Forget the vessel. Let's blow out all the air, patch up the hull, and replace the vacuum with water.
What's the pressure inside?
Well, when you first start filling it with water, the water will boil into steam - if you look up a tri-state chart of water, you'll see that for low enough pressures, you simply can't have liquid water: it'll either boil or freeze.
But as more water is added, something weird starts to happen. Eventually, the pressure of steam will get high enough that water starts re-condensing and the water you're adding won't be boiling off. If we were in an environment with gravity, we'd have a layer of water on the ground and a layer of high-pressure steam above it. But gravity isn't in this picture (ISS!) Instead, we have water and steam intermingling - and since water has some good surface tension, we'll generally see globules of water meandering through the steam.
As we add more and more water, the pressure goes up, the volume taken by steam goes down, until eventually the entire ISS is filled with water with no steam. And that water is just above the condensation pressure for water. In real-world terms? It'd be what water is like at the surface of an ocean/pool/puddle.
... and as you add more water? The pressure starts going up. You're adding more water molecules, but not giving them any more space. And given how incompressable water is, the pressure starts to climb pretty rapidly.
And like the plunger situation (and assuming ISS was built out of infinitely strong material) you'll have a situation where, when you added enough water, you'd cause the water to start solidifying due to presure.
T.E. #3 - Giant Plunger
Imagine you've got the same cylinder and plunger from the first thought experiment, but this time: They're huge. Once again, you press down superhumanly hard, and barely condense the water into ice.
What happens when you let go of the plunger?
On one hand, Ice VI and Ice VII have a density either 30% or 50% greater than regular water. So if a chunk of regular water would be pulling with 10 newtons of force due to gravity at N meters, a chunk of Ice VI or Ice VII would be pulling with 13-15 newtons.
Now, think how little this difference of gravity would be... versus how great the pressure difference would be! Imagine how much force a column of water 100 kilometers deep would push down on you? That's how much force the ice would be trying to exert in order to expand.
In other words, the plunger would go flying away from the ice - the ice would be pushing with immense force - far more than its slightly higher gravity would hope to counteract.
Putting Everything Together
As the OP guessed at: long distance gravity wouldn't matter much. If the universe was simply infinite ocean, the gravity would have no net direction/force.
But that's not to say there wouldn't be pressure. Like our ISS in Thought Experiment #2, it all depends on how many water molecules there are in a given amount of space. Not enough: no ocean (its all steam.) Too much: sea of exotic ice. Just barely enough: water with pressure like you'd find at the top of the ocean. Almost too much: water with pressures greater than any ocean trench.
Now, something stirs up 'space' - such as the pull of a local dense object. You've effectively got a plunger pushing downward on your water. If that object isn't very big? You're just lightly pushing down on the plunger - until the pressure from the water is equal to your force. If the object is really dense and massive? Then the plunger is pushing down hard enough to solidify the water around the surface to exotic ice... but ultimately it's like our T.E. #3 - that ice has enormous amounts of force that it's using to try to expand.
So, TLDR: The water's going to be pretty uniform: water pressure is much stronger than increased gravity from denser water. Even dense non-water objects will probably simply have a gradient of increasing water pressure - and possibly exotic ice - around them.
Finally, to the OP's question: what would a solid experience in that environment? Figure out what the pressure would be (dependent entirely on how much matter there is per volume) and then ask yourself: how would an object under the surface of the ocean act (assuming the object has the same density of water, since gravity doesn't play a role.)