The Taylor Institution Library has a linguistics reading room with full runs of journals on open shelf and a lending collection on general linguistics where you may find recent acquisitions, frequently used items and reference works. Many other titles are held in closed stack and may be requested for lending through SOLO.
The Teaching Collection (formerly Modern Languages Faculty Library) has a good lending collection including reading list books. English linguistics are in the English Faculty Library, classical linguistics in the Sackler Library, Slavonic linguistics in the Slavonic library. The Radcliffe Science Library holds a collection on child language and language acquisition as well as materials on phonetics. Applied linguistics are in the Education Library.
SOLO - the online catalogue. Use to find books, conference proceedings, journals, e-journals, e-books, etc. that are available in Oxford. SOLO will also give article or working paper titles. For a more comprehensive search for articles, see 'Articles & Working Papers'. SOLO will link through to OLIS when 'check library holdings' for a specific title is selected.
If a book or journal isn't available in Oxford, try finding it elsewhere in the UK through COPAC, the online catalogue for UK academic libraries. Titles may be requested through InterLibrary Loan. COPAC is more comprehensive for the UK than WorldCat. However, if a title isn't available in the UK, try and locate it elsewhere in the world through WorldCat and place an InterLibrary Loan request.