I've noticed whenever I write my own songs, they kinda sound similar to songs from my favorite bands. They do sound noticeably different at the same time though.

Is this normal?

Or am I just picking up an unusually large amount of inspiration from my favorite bands and songs?
yeah, that tends to be normal.
Gibson Explorer - White
PRS SE Singlecut
Fender Acoustic

Crate head w/ POD preamp
Crate 120 watt POS
Crate Cab
^ +1

the more you listen to and let influence you the more variety your songs will have. i started out listening to nothing but metallica and pantera and now i have a blues song (yet to record) an entirely orchestral piece and even an old country sounding song. keep writing songs and even though it might take awhile you can rest assured that eventually you'll find your own sound.
Just start listening to different bands. Find one or two bands from each genre.

It's normal though, it's only a problem if it's deliberate.
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