An example of a code that is neither p-code or s-code but is uniquely decodable?
An easy way to get new codes of any size is to compose a prefix non-suffix code and a suffix non-prefix code. For instance, start with the prefix non-suffix code $X_5 = \{0, 10, 110, 1110, 1111\}$ and compose it with the suffix non-prefix code $\{0,01\}$, which consists to replace $1$ by $01$ in $X_5$ to get
$$
S_5=  \{0, 010, 01010, 0101010, 01010101\}.
$$
The resulting set is a code that is neither prefix nor suffix. 

N.B. The advantage of this method is that you always get codes, no verification needed.