"avenues by which" is a perfectly correct and usable phrase in written English.
You can use it to describe various paths or methods you can use to reach a certain goal or outcome. For example, "We explored different avenues by which we could make our business more efficient."
There are, however, other avenues by which the body can be oversupplied with thyroid hormones.
There are two jurisprudential avenues by which the justices could make gay marriage a constitutional right.
They argue that public debate constitutes one of the main avenues by which citizens can participate in collective decision making.
In fact, there are a number of avenues by which the US will be able to exert military influence in the country.
Clearly there is little money to be made in selling records these days, and touring is expensive, so why begrudge artists (and their labels, who love money) new avenues by which to make some extra cash?
Maybe it is understandable on the part of the mother, Sally Faulkner, who believed she had few other avenues by which to gain access to her two young children, taken to Lebanon nearly a year ago by their father.
They noted that this "provides a likely avenue by which brand loyalty and product preference can be built".
Support the human rights organisations determined to shut down every avenue by which the regime can legitimise itself.
But the eggs, at least, offer an avenue by which Warren might just out-cool his Hollywood antecedent.
"We are looking at every possible avenue by which the different functions of banks can be brought back into being," he stated.
In opera, servile imitation of nature is dispensed with…here is…the avenue by which the ideal can steal its way back into the theatre.
