There are three differences between monopolistic competition and oligopoly.
The first, and perhaps least important, is the difference in the type of product that they make. An oligopoly can produce either a homogeneous product or a differentiated product. That is, it can be a product like gasoline, where there is no real difference between one brand and another, or it can be like soda or cereal where there are real differences. Monopolistic competition only occurs when the product is differentiated.
Second, there are relatively high barriers to market entry in an oligopoly whereas the entry into monopolistic competition is relatively easy. Auto makers are an oligopoly as it would be very expensive to start an entirely new car company from scratch. By contrast, small restaurants are easy to start and are an example of monopolistic competition.
This factor leads to the third factor, which is the number of sellers. Since it is easy to enter a monopolistic competition, there are many sellers in such a market (many small restaurants in every town). By contrast, it oligopoly, there are only a few large sellers (think of how few automakers there are).
These are the main differences between these two market structures.