I understand white oil or olive oil are commonly used for aphids as they will sort of drown them out. Neem Oil can also be a good choice, it breaks down quickly and neem leaves are used in medicine as well as in the production of certain products for diabetics, so I am pretty sure it is perfectly safe. You will have to spray whatever oil you use fairly generously on the leaves.

Lady bugs, they do well in my garden! Depending on your size, I sprinkle them all over everywhere in the morning right after I have watered!