Is it normal that i have a different voice around my dad than other people?

Tell me, what does a pile of burning sticks sound like?!

Some people just do.

I have a kind of flat, nasally voice with sharp pronunciation but when I'm tired or in a bad mood it drops to an almost creepy, uneven drawl.

Well, your questionable choice of terminology aside, it is actually normal to have different speech patterns around different individuals and groups. There are many reasons behind the changes, and can be dependent on relationships, class, culture, and profession. The most notable difference is not only the tone of voice, but the change of phrasing and vocabulary. Linguists even have a term for it, it's called "code-switching!" So no worries, it's normal!

However, if you are uncomfortable with the difference, it may help to pinpoint the reasoning behind it- and whether it's really of help to you to make that switch.

Maybe your dad makes you feel inferior.

How do you mean like a fag? I don't know if you mean more feminine or???