Can someone intuitively explain the reason for the units of entropy (J/K )?
The units of of energy over temperature (e.g. J/K) used for entropy in the thermodynamic definition follow from a historical association with heat transfer under temperature gradients, in other words, the definitions of temperature and entropy are intertwined, with entropy being the more fundamental property. Entropy can be thought of as a potential and temperature (or its inverse, rather) as a generalized force associated with displacements along energy dimensions in the entropy potential. The (inverse) temperature is a measure of the effect of changes in the amount of energy on the entropy of the system, as the following definition suggests:

$$\frac{1}{T}=\left(\frac{\partial S}{\partial U}\right)_V$$

However if you start from a statistical mechanical definition of the entropy, 

$$S=k_\mathrm{B}\log\Omega$$

then it is easy to see that a unitless definition might be just as well suited:

$$S_{\mathrm{unitless}}=\log\Omega$$

However, in the absence of the Boltzmann constant you need some other way to relate entropy and energy (e.g. heat transfer) in our conventional system of units. You can of course subsume $k_\mathrm{B}$ into the definition of a new temperature scale:

$$\frac{1}{T_\mathrm{new}}=\left(\frac{\partial S_\mathrm{unitless}}{\partial U}\right)_V$$

where the old and new temperature scales are related as $T_\mathrm{new}=k_\mathrm{B}T$. The new temperature scale then has units of energy.