first things first - a dx isn't going to change the behaviour. at all. and you may or may not be offered support as a result of the dx, so it will be helpful if you can try and inform yourself as much as possible and try to implement some things that will help. waiting until you receive a dx is fine, but won't really help.
second - is it just you dealing with the 4 children, or is there a dp around to share the burden?
third - what do school say? how does he behave in that setting? have you met up with the senco and class teacher/ ht - do they have support in place for him? (you said he had a medical last week for a statement but where are you in the statementing process? have you or school applied?)
fourth - what dx are you expecting from camhs? you have a dx of developmental delay - are you expecting them to confirm adhd and some specific behavioural issues? or is the doctor veering more towards learning disabilities or spectrum disorders?
fifth - are you receiving any external support? home start can offer you a volunteer as you have children of the right age group and are struggling to cope (even if the child in question is older) - has anyone suggested applying for dla (notoriously difficult to get in this sort of case, but sometimes possible). are you in touch with any local sn support groups? there are usually parent groups for all sorts of things - if you have a sure start centre that's usually a good place to start.
nothing is going to change overnight, so you need to try and work out how you can get yourself into a stronger place. obviously there are meds etc that can be trialled to deal with certain issues like hyperactivitiy and distractedness, but they aren't always suitable and are not always effective. a dx will give you some clues as to what might help, but it isn't going to be straightforward, so you need to conserve your energy. lots of sn parents find that the constant battles wear them down and so take 'breaks' from trying to find solutions/ get support, to recharge. some find anti-depressants take the edge off the constant fighting and allow them to see a little more clearly. maybe it would be worth discussing with your own gp what he can suggest to give you a helping hand? (not necessarily meds - he may have inroads into support networks or counselling programmes)
the path to dx is pretty rough for lots of people. there are a few 'road to dx' threads running i think, so you might find a nice home on one of those alongside people who are having similar experiences.
you aren't alone, honestly. i'm sure someone will come along with some concrete ideas for the behaviours you describe (i'm only familiar with the use of a 'safe space' to prevent destruction and damage to people or property, but i'm not sure whether you are already utilising this idea where practical in the home.)
sorry, that's really rambly, but might help you set out exactly where you are and where you might be able to go next.
i'm assuming you are living in an area where you do not have access to multi-disciplinary assessment centre or developmental paediatrician? so cahms is the dx source? (it varies across the country)
and vent on here whenever you need. there's usually someone around. 