Oxymorons make use of two seemingly contrasting words to express something in a more emphatic manner. The apparent contradiction rests in that fact that, if analyzed individually, the words would indeed present opposing meanings. The contradiction, however, is not entirely so. It makes sense according to the context and, as stated above, its purpose is to emphasize an idea or to express the confusion or ambiguity of the moment. That's what we can notice when analyzing the oxymorons "pretty ugly" and "bittersweet", respectively.
In "pretty ugly", "pretty" is merely intensifying the adjective "ugly". In "bittersweet", the opposing words show conflicting feelings. We may use them as the following examples show:
I don't understand art at all! That picture was sold for thousands of dollars and it looked pretty ugly to me!
The day I left my parents' home was bittersweet (meaning I was happy and sad at the same time).