a girl wrote me this:

"Ben de çok özleyeceğim"

and then sad face. what does that mean?

thank you!!

It means: I will also really miss you. 

Although she forgot the seni

@denzili

Can it be used without the ´seni´ or does that seem odd in general?

As a Turkish native speaker, it seems odd to me. If someone is missing "you".

But if someone is missing "He, she or it", (Or Turkish "O"), in a context like the one in the below, it is not so odd.

Onu özleyeceğim. (I will miss him/her/it.)

Ben de çok özleyeceğim (I will miss, too)

Grammatically it´s not correct - özlemek requires an object. 

For conversation, I don´t know the answer.

When things are missing it´s hard to guess. But I´m sure Cymanteg´s answer is correct.