I just turned 18 two days ago and my girlfriend of 6 months only turns 16 in February. She lives in Texas until June, and the age of consent in Texas is 17. But she's moving back to Oklahoma in June and the age of consent law is 16. But her father is threatening to press charges as a sex offender if we have any contact? But I am not doing anything wrong by just talking to her right? As long as there is no sexual conversations. We are in love and are fighting this, I'm willing to have no sexual relations with her until it is legal. So therefore he can not charge me with anything right?

The parent can charge you for various things if you as a adult will not leave his child alone after he tells you.
Interference with Custody is the easiest one. So as a adult, you can be ordered to leave a minor child alone, if you don't, just being with the child can get you into legal trouble.

But also many states have their own separate laws for same sex relations, some are the same age, others the ages differ, so age of consent to have sex with someone of other sex, is not always the same age for same sex.

You risk your own freedom when you go against a parent who tells you to leave their child alone, in any state.

Its called Custodial Interference. Having sex would be the least of your worries.

As far as I know, which isn't very much, in Texas interference with custody and custodial interference do not cover conversations AS LONG as the conversations in no way express intent for you to take her away from her dad. Here are some links supporting this.

http://www.statutes.legis.state.tx.us/docs/PE/htm/PE.25.htm

http://penalcode.austintexascriminaldefense.com/25.03.html

http://myfamilylaw.com/library/children-parenting/custody-visitation/faq-what-does-custodial-interference-mean/

However, this is mostly because those laws seem to deal exclusively with non custodial parents. Fr_Chuck's statement that there are other things you could be charged with may be true.

As far as I can tell, though, if you are talking to her online and your conversations are not sexual, you cannot be charged with Online Solicitation of a Minor. Read Sec. 33. 021. Of the following link.

http://www.statutes.legis.state.tx.us/docs/pe/htm/pe.33.htm

While I understand your desire to be with her, maybe give her dad some time to get used to the idea and feel safer with you. You don't want him to feel powerless or disrespected.