How would you differentiate between "I will speak to her - Θα της μιλήσω" and "I will speak with her"?
I will speak with her=Θα μιλήσω μαζί της/με αυτήν.
Talk to means one-way conversation, talk with her is 2-way. Is that the difference in Greek, too?
Yes. Θα της μιλήσω means that I will tell her something I want. Θα μιλήσω μαζί της or Θα μιλήσουμε (or better still θα συζητήσουμε) implies a mood for a two-way conversation.
Θα της μιλήσω.
Θα μιλησω μαζί της.
Θα της λεω(?).
Θα μιλήσουμε της.
Θα συζητησουμε της.