I have four 6 1/2 week old dachshund, all of them are dry heaving and periodically throwing up white foam. There is also a 6 month old dachshund that is at our house a lot that also vomited white foam last night. They are all still eating, drinking, playing, and going potty normally. I just don't know if I should be worried and I can't afford to take them all to the vet.

Most commonly, your dog has been eating grass :)

They do this when their tummy is upset.
You could try a different food. Are you feeding them PUPPY food? Even the 6 month old should be on puppy food till he is 1 year old.

Other than that, if they are playing, eating pooping peeing as normal, I would say don't worrie unless they start throwing up FOOD and/or stop eating/pooping

Purging, eating grass and throwing up, is not unusual in early summer. Keep a close eye on their fluid intake. If they start guzzling water it can be as bad as stopping drinking and needs an immediate vet visit, even if you have to set up a payment plan.

The white foam can also happen on an empty stomach. You might want to try smaller meals, more frequently - if they are only eating once or twice a day.