I'm a retired teacher who is now subbing. I've been in hundreds of classrooms--every grade level--over the last three years as a sub, and it has been quite an education. I've been in good classes, bad classes, and everything in between. I've had the opportunity to talk to a number of teachers and observe (and try) a number of strategies. I've had quite an education in retirement!
I really can't diagnose from my computer, but it sounds as if your seven students might have ADD. I've had numerous kids like this, and they have a very hard time sitting still and concentrating. They can be absolutely infuriating to a teacher, even if they aren't behavior problems. Still, there are a few things that can be helpful. I'm not promising that these suggestions will solve all the problems, but they may help.
1. If your principal will allow it (and some have suggested it to me), send these kids every now and then on an errand, even if it's a fake one. I've done this on occasion--sending them with fake notes to the office, but telling them that the notes are important. Having these students get up and move around (and making them think they're being helpful) in this way can help.
2. Have the kids get up now and then to stretch. I really like the basic Brain Gym movements; perhaps there is a teacher in your building who is familiar with them. I've found that sometimes restless students or students who can't concentrate do a little better after these movements. Be careful, though, with certain exercises. I've found that doing things like jumping jacks gets the kids more wound up and less able to focus.
3. If these students can't concentrate on a long spelling test, try breaking it up into two smaller tests (I tried a variation of this idea in my own classroom with some success). Could you possibly give a ten word spelling test on Wednesday and another ten word test on Friday? As far as your reading test is concerned, could you possibly give two short reading tests instead of one longer one? Could you possibly give shorter tests, but test more frequently?
4. Moving from one activity to another every 30 to 40 minutes can also be helpful.
I cannot guarantee that all of these suggestions will work. However, if you are ever questioned about what you have done for these kids, you can always say that you have implemented a number of well-accepted strategies.