The best place to store your luggage in Delhi is the Cloak room at the railway station. All you need is a connecting train ticket. Even if you are not travelling by train at any time, get a cheapish train ticket to be able to store your gear in the cloak room. I have done this several times while transiting through cities. Hassle free and super convenient. Alternatively, several hostels in Delhi will be able to help you with luggage storage (for free or at a nominal price). Madpackers is one good option. Get in touch with them and discuss in advance, so they can make any necessary arrangements, if needed.