We had the same problem a few years ago. Our neighbors house was literally infested with them.... to the point that the state came in and took the children and considered the house unlivable! Unfortunately we found out fleas travel! In the neighbors case they actually had to call in professionals who ran out of the house doing the heebyjeeby dance and were covered in 15 seconds! They came back with Tyvek suits and respirators... there was also rat problems! It was disgusting... but goes to show you just never know about your neighbors!
When I noticed our dogs scratching and my son who I also thought had mosquitto bites was bitten by fleas I went and spent a small fortune on the flea stuff from Petco... bombs, sprays, baths etc... none of them worked and the fleas were still here...Grrrrrr ! They go for a certain blood type I found since my husband was the only safe one in the house!
I finally called the vet who told us not to waste money in all the products out there except for the Frontline we got from him. No need to bomb the house or call in Orkin- which was my first thought! We were to just vaccuum every day in the morning and night and as the fleas jumped on our dogs they would die off. It took about 2 days until we did not notice any problems with itching and I did not see anymore of those nasty things!. The good thing- no harsh chemicals in our house!
I would not worry about your sons stuffed animals since they do not have blood and if they are on them they are just traveling through to get to the dogs or cat and once they go to the vet will die once they hitch a ride on the dinner train!! Watch your son for bites. Not sure of the age recomendations for Off but we all (except hubby) wore Off around here which stopped us getting bit for a few days.
Ohhhhhhhhhh now I need to go shower since I feel like I am crawling with bugs! Ughhhhhhhhhhhh Good luck to you and many blessings!