You could do that in a one-liner using generators:
next(i for i,v in enumerate(l) if is_odd(v))
The nice thing about generators is that they only compute up to the requested amount. So requesting the first two indices is (almost) just as easy:
y = (i for i,v in enumerate(l) if is_odd(v))
x1 = next(y)
x2 = next(y)
Though, expect a StopIteration exception after the last index (that is how generators work). This is also convenient in your “take-first” approach, to know that no such value was found — the list.index() function would throw ValueError here.