Both my children have had these allergies and I always really appreciated it if people provided things for them at a party, so bless you.
You could ask the mum whether the child tolerates soya lecithin - it's in a LOT of things and some children with soya allergies tolerate it (others don't) so it's helpful to know.
My son loves party rings, they are dairy-free but I can't remember if they contain soya lecithin or not.
We also bought a lot of Mrs Crimbles madeleines, they are dairy-free and soya-free, and taste pretty nice. Plus individually wrapped which is handy.
Most savoury food is fine, if you are doing sandwiches then it would be appreciated if you could use soya-free bread and dairy-free spread, then the child could eat any sandwich as long as it doesn't have cheese in it.
Pom bears are fine and always go down well.
Jaffa cakes - Own brand tend to be fine but the McVities ones contain dairy.
Basically you have to check the labels very carefully!
If you buy anything please keep the packaging so the mum can check it herself. I like to do this for peace of mind because it's so easy to miss things (DH and I still mess up sometimes). I hope no one is offended when I check!