You might find this Oxfordshire County Council page on applying for a school place useful: www.oxfordshire.gov.uk/cms/content/transferring-or-moving-different-school
If your son turned 5 after September 1, then he would join a Reception class. If he turned 5 on August 31 or before, then he would be in Year 1. While there are new arrangements that parents of summerborn children can apply for a deferral, I'm not sure this can be done retroactively. You would need to speak with someone at the Council admissions team.
Catchement area will not really mean anything for an in-year application, your son will be offered a place at a nearby school where there is space. Schools may only take up to 30 children per class in the younger years.
I can only guess where you are, but the schools nearest to you are probably Phil and Jim, Wolvercote, St.Aloysius (Catholic) and Cuttleslowe.
If you are not happy with the school your son is assigned you may: a) enrol him at the assigned school until a place at your preferred school become available, b) enrol him at a private school, either temporarily or permanently, or c) home educate, either until a place becomes available, or as long as you wish.
Your will apply for your daughter's school place in Autumn 2017 and she will start school in September 2018. She will be eligible for 15 free hours of nursery/preschool a week the term after she turns 3, so the beginning of January.