Bear in mind that there is indeed a formality in Japan that doesn't exist in English. In other words, its OK to be somewhat formal, even among friends and colleagues and family members - especially when you are asking them to do something for you. Formality is embedded into the language, and its not unnatural in any way. Trying to be casual can, in fact, make you sound imperious.
In addition to ~kudasai or ~onegaishimasu (note these are not exactly interchangeable) you could pose as a question, which might have a softening effect
~kudasaimasu ka?
~onegai dekimasu ka?
~してもらえますか? "Can you do (something) for me?" is also fairly neutral, but depending on the relationship of the asker and the do-er, there could be an implication of presumption.
But, I suggest you embrace the formality.