I have used shampoo bars in the past and they have made my hair oily after use. Why?

This could be for a couple of reasons:

1. In order to formulate a great bar, ingredients need to have a high HLB (Hydrophilic–lipophilic balance). This allows the shampoo and conditioner to wash off the hair readily and not leave a grimy residue. 

2. The type of surfactant (cleaning agent) used is important. Some surfactants clean too well and excessively stripe oil from the hair. In response the body will produce extra sebum to compensate.