The definition of an even function is $f(-x) = f(x)$.
The definition of an odd function is $f(-x) = -f(x)$.
A periodic function means that for a fixed number $P$, $f(x + P) = f(x)$.
Therefore, substituting $-x$ in for $x$, $\sin(-ax) = -\sin(ax)$. This matches the definition of an odd function, so $\sin(ax)$ is odd.
To find if it is periodic, draw a graph of $\sin(ax)$ (I used WolframAlpha) and see if the graph repeats itself at all. In this case it does, every $2\pi$. Therefore the period is $2\pi$.
Try this method on the other functions and you should find it easy :)