무슨 is what but after what, have to follow noun. for example 무슨 일이야? what happens?
어떤 using is depend on the situation , how or which, but more like which. and the answer is requested Adjective. for example
어떤 남자가 좋아? 멋있는 남자가 좋아.
어느 is which. but normally we use this when we have options. we don't say 어느 날씨가 좋아? but 어떤 날씨가 좋아?
for example. u have many many kinds of shoes, 오늘은 어느 구두가 좋을까?
and this is other meaning, also we use it for one day->어느날
However, i think nowadays many people don't distinguish 어느 n 어떤, so you can use 어떤 instead of 어느, but not to use 어느 instead of 어떤. it means range of 어떤 is a bit bigger then 어느.