"All the schools I'm applying for are very oversubscribed. The school I like least is the one I live nearest to. Should I put it last on my list?", yes, and you should make sure that that s a school you have a good chance of actually getting a place in. if there is not a school on your list that can offer you a place based on it's published admissions criteria, the LA will offer you a school, any school, that has a place after everyone else's places have been allocated. You can't play the system by only listing popular oversubscribed schools on the understanding that 'they will have to give you one of them'.
"The law requires admission authorities to meet parental
preference wherever they possibly can."
This isn't contradictory - it is a supplementary confirmation of the system. The schools tell the LA which pupils they can admit, base on their particular criteria (distance, lottery etc) and the LA must then offer you whichever of those places is highest up your preferences.
The LA couldn't, for example, say 'Oh, sorryforher has been offered places at her second and third preference schools, so let's give her her the third choice one, as that is undersubscribed and we need to take pressure off the second [listed school to make way for parents who named it first'. That is what the equal preference system is all about.
List the schools in the exact order in which you genuinely prefer them.
Is the very over subscribed school that you like least your closest school? If not, is there a good chance you will get a place?