Why are oxygen and hydrogen compressible, but water is barely compressible What makes the two gases compressible, but does not apply to a liquid like water?
 A: The force between two (non-reacting) atoms is approximately given by the Lennard-Jones potential, and this varies with the separation of the atoms something like this:

(this image is from the Wikipedia article I linked above). In the diagram the parameter $\sigma$ can be thought of as the size of the atom, so the value on the $x$ axis of $r/\sigma = 1$ is the point where the atoms come into contact. When the atoms are far apart there is a very slight attraction, but as soon as the atoms come into contact there is a strong repulsion and it's very hard to push the atoms any closer together.
Be cautious about taking this too iterally as atoms are somewhat fuzzy objects and don't have an exact size. nevertheless the point remains that there is a distance between the atoms at which they suddenly start to strongly repel each other.
Now back to your question. For nearly ideal gases like oxygen and hydrogen at standard temperature and pressure one mole (that is $6.023 \times 10^{23}$ molecules) occupies about 22.4 litres. This means the average spacing between molecules is around 3nm. The size of an oxygen molecule is very roughly (they aren't spherical) 0.3nm, so the spacing between the molecules is about 10 times their size. That's way off to the right on the graph above, and it means the forces between them are low and it's very easy to push them together. This is why gases can be easily compressed.
Now conside water. One mole of water (0.018kg) occupies about 18ml, so the spacing between the molecules in water is about 0.3nm - in other words they are in contact with each other. This is the point where the molecules start to repel each other stringly, and that makes it hard to push them closer together. That's why water is not easily compressed.
You ask about compressing a mixture of (unreacted) oxygen and hydrogen. Well if you compress oxygen enough it liquifies, and the density of liquid oxygen is about 1140 kg/m$^3$. This makes the spacing between oxygen molecules about 0.35nm. This spacing is about the same as the size of the O$_2$ molecules so it's hard to compress liquid oxygen. You can repeat this calculation for liquid hydrogen (density about 71 kg/m$^3$) and you get a very similar result. Actually I would expect liquid hydrogen to be more compressible than liquid oxygen and water because the H$_2$ molecule is significantly smaller. However a quick Google failed to find values for the bulk modulus of liquid hydrogen.
A: The average density of liquid water is about 1000 $kg / m ^3$. The average density of air is about $1 kg /m^3$. So liquid water is about 1000 times denser then gas. When you compress liquid water together, the molecular forces become very strong stopping it from being compressed very much. However, for a gas the molecules are so far apart that the forces are much smaller (the main reason a gas can't be compressed is due to the kinetic energy of the molecules in the gas).
A: The basic model of a gas that individual gas particles don't interact. As in: there's enough space between molecules, such that they spend most of their time travelling in straight lines, without bumping into each other i.e there's lots of space between particles. With this in mind, it's not surprising that a gas is compressible.
If you compress your gas enough (and lower the temperature), eventually the particles will come close enough that they start to attract each other, and then your gas turns into a liquid. You can't compress a liquid as much simply because there isn't as much space between particles.
In summary
Gases: lots of space between particles --> compressible
Liquids: very little space between particles --> not compressible
