Is it correct and similar to say :

[nomesperesenabril]

I don't have any computers or pictures in my room.

I don't have neither a computer nor a picture in my room.

[emsr2d2]

I don't have any computers or pictures in my room. This is fine.

I don't have neither a computer nor a picture in my room. No. You have used a double negative (don't and neither in the same sentence). You can say either:
-I don't have a computer or a picture in my room.
- I have neither a computer or a picture in my room.

See above.

[nomesperesenabril]

what about : I have neither a computer nor a picture in my room.

[philadelphia]

what about : I have neither a computer nor a picture in my room.

You are right - neither [...] nor. I assume the above poster made a typo