The three are all ok and natural.
Probably, the last - "I like tea but don't like juice" sounds the *most* natural to me if you are only making a general statement or observation. In casual conversation we tend to drop words where possible and here it's "I" (before don't).
Keep in mind the three aren't completely interchangeable. If someone offered me a choice of only 'tea or juice', I would choose the one of the first two expressions. While the 3rd would work, it just doesn't sound as natural in this particular context.