I really like Smashing Pumpkins, The Pixies, Cage the Elephant and similar artists for their lyrical and musical style. I wanna try writing lyrics (and music) in a similar style without being a complete ripoff. But either way I try writing it sounds like a ripoff =\

So yeah, what should I do? I don't write that often, so I know doing that will help a bit.
man you can mix your influences and make it sound, with your personal touch, totally different...
There are generally two parts to writing: your influences and your influence. Subtle difference there, but the mix of those two categories results in a creation that is totally unique.

Plus it's basically impossible to write without "ripping off" someone else to some extent. It's basically the "THE SIMPSONS DID IT" scenario. Bands have been ripping off bands who have ripped off bands who have ripped off bands who have ripped off bands. (inb4xzibit)

Try not to worry about how much your influences shine and worry more about writing something you can enjoy.
Just go for it man. Learn your favourite songs, read books, watch movies. Absorb everything.

The new Cage album sounded Pixie-esque, but it was still Cage. Nobody can play YOUR music, ultimately.

Try not to think so much. That would be my advice, not just for music but in general to.
As people have said, the more writing you do, the more you will develop your own style. But, there's a great quote that goes something like "good artists borrow, great artists steal." When listening to newer rock songs inspired by some of the greats, such as the Beatles, I often hear little melodies that sound very similar. If you hear a melody in a song and you're absolutely crazy about it, what you can do is look at WHY you like it so much. Is there a certain interval between the notes that makes you go nuts? If so, you can steal the "concept"behind the structure of the melody. But basically, the more you write the more you develop your style. It took me years and 2 full demos before I actually developed a style original enough to make an album and call it original. Takes time but it's worth it.