The phrase "at varying degrees" is correct and usable in written English. You can use it to describe something that changes or varies in intensity or degree. For example: "The students had varying amounts of experience, ranging from complete newbies to experts at varying degrees".
Under the agreement both pensioners and bond holders will take pain, albeit at varying degrees.
The following, however, are categories in which measurement at varying degrees of precision is involved.
By the turn of the century, the Germans, Austrians, Italians, Russians, and Swiss all had ski troops, at varying degrees of readiness.
It offers inn-to-inn tours or day walks from one hotel, at varying degrees of difficulty (a moderate trip features a total of 70 miles of walking).
The image before us was a series of circles in pairs, overlapping at varying degrees from just barely touching to completely merged.
He suggested making several copies of a photo at varying degrees of darkness and printing them all to see which looks best.
Its spa, open to budget-conscious day visitors as well as hotel guests, is a pink confection of Art Nouveau and endless rooms, each containing mineral pools pitched at varying degrees of nice warm bath.
Ludwig does not simply clarify my doubts with English writing, it enlightens my writing with new possibilities
Simone Ivan Conte
Software Engineer at Adobe, UK