If these are infant class size cases you have very little chance of success unless you can show that a mistake was made in the admissions process and your son should have been admitted. If any of them are not infant class size you have a better chance of success.
Some basic do's and don'ts for you.
Do read the LA's case thoroughly and make sure you understand it before the appeal.
Do ask the LA questions if there is anything you want to know. They will be helpful even if the information they give you undermines their case.
Do find out the capacity of the school and the current number of pupils. If the school is not currently full that may help you to argue that admitting your son will not cause prejudice.
Do concentrate on needs your son has which can only be met by your chosen schools. These could be educational, social, medical, physical - anything that says he needs to go to this particular school.
Do read the other recent threads relating to appeals. They contain a lot of good advice.
Do submit all relevant documents before the appeal. If you produce significant new evidence at the appeal you may find that the appeal gets adjourned to allow the LA and the appeal panel to absorb it.
Don't take a photo of your son to the appeal. That could turn the panel against you as it feels like a form of blackmail.
Don't talk about league tables, OFSTED reports or anything else to do with the quality of education provided. I'm afraid that isn't relevant and may turn the panel against you.