The academic jobs market is most active from September to March. If you are considering an academic career it’s a good idea to familiarise yourself with this annual cycle as soon as possible (at least in the third year of your PhD and preferably in your second year). You should take it into account when planning your submission and viva dates. The major postdoctoral schemes (British Academy, Leverhulme and so on) have deadlines around the same time each year. Advertisements for Oxbridge JRFs start appearing as early as September. Some postdoctoral fellowships are open to applicants still doing their PhD, others are not. If a PhD is specified, there will be no point in applying without one, so be guided by their statements. In April/May of the year before you wish to start making applications, you should draw up a list of the forthcoming deadlines of all the post-doctoral schemes for which you wish to apply. Then you will have a clear sense of the lie of the land and won’t miss any opportunities.
There is little point in applying for any permanent lectureships unless you already have your PhD, or at the very least, if it’s a junior lecturer post, you have submitted and know the date of your viva, which should be well in advance of the start date of the job. Most lectureships are advertised from January to March, although there may be some earlier and later (especially temporary posts).