this probably has NOTHING to do with being organic but it has worked wonders for us and we have 2 small dogs that it doesn't harm. The AMDRO granules from home depot or Ace. That stuff is amazing! $15 well spent. Killed all our Fire Ant problems. We had an infestation on our property (in and outside) and next door neighbors too. Now, they're all gone.

Try Tanglefoot. It's a sticky substance like flypaper painted or sprayed around the trunk, stops the ants.

I don't know if it works with fire ants (and you didn't say that's what you've got), but I've used a mix of borax (from the laundry aisle), sugar, and water for years. The ants eat it, carry it back to the nest. It takes a few days to kill off a whole nest. There's at least one commercial product, Terro, that's pretty much the same thing, but making your own is cheaper. And you can use the extra borax to get your clothes clean, too!

The insecticidal soap or oil will probably control the aphids better once the ants are gone. Incidentally, more ants will come in once a nest is gone, so you have to keep treating.
good luck!