Is there a list of all airways?
Airway data is published in each country by their respective regulatory authority. This is published as a part of AIP(Aeronautical Information Publication).

This page contains links to some of the sites having electronic AIPs. The relevant data can be found in Part 2- Enroute(ENR). For example, this gives the details for UK airways.

I don't think there is a worldwide list as the airways of each country is controlled by the respective government through regulatory body and this information is updated periodically (in cycles of 28 or 56 days).