Repulsion among air molecules

Q: When the spaces among molecules decrease to a level that when the electron clouds overlap, what will happen?

A: The molecules will rebound from each other. This is the process of elastic collision between molecules.
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Q: Will the molecules turn into liquid state?

A: Molecules themselves WILL NEVER turn into liquid. The states of matter refer to the phase that experienced by a substance (or a matter). It does not apply to molecules. Molecules always remain as molecules irrespective whether the substance is in the solid, liquid or gas state. It is only in the plasma state (the fourth state of matter) that molecules are ionized to become ionized paticles.
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Q: Lets assume the molecules continue to approach without being repelled. What will happen?

This is physically highly unrealistic. Molecules need a tremendous high energy in order to come to a distance shorter than one molecular diameter. The more closer they approach, the more energy is required. Generally, normal thermal energy (i.e. energy that depends on temperature) is not great enough to make molecules come to distance shorter than one molecular diameter, unless the temperature is as high as that in the centre of the sun that fusion of molecules could happen.

Should this happen, just as an imagination, the very strong electrostatic repulsive force given by the positive charged nucelii of the atoms would prevent the atoms to approach further. This is the reason why neutron, being an uncharged particle, is used in nuclear experiment and in nuclear fusion to bombard atoms. This is to avoid encountering the strong electrostatic repulsive force of the nucleus.