Google forms would do that for you. You can set up the form as open to anyone with the link - or make it so that they don't have to sign in. Just make sure that your first question is a compulsory question asking for their name. Then use flubaroo to mark it.
There are a lot of collaborative things that you could still do with google apps - just set up a class google account that has a shared login. Teach the kids that on a shared doc they all must write in their own colour, or write their name after any entries. If you have classroom computers it could stay logged in on them.
Google classroom takes a lot of the hassle out of sharing the files, but there is still so much you can do without it.
You could also set up a class website (with google sites, or another platform).
Oh, and the showbie app is a great way to really quickly share docs, pdfs etc to the kids and they can write on them. It is an ipad app, I don't know heaps about it though as I use hapara to send everything out to my kids. But showbie might work as a solution if you have ipads. the kids can send stuff back to you to be marked.
I love WEO! The only drawback is that it seems to take a ton of bandwidth, which was a problem when we had two classes using computers at the same time.
You also couldn't return assignments for redo easily - you could either tell them which ones they got wrong and give the answer OR return the assignment without answers but not tell them which ones were wrong. But they seem to have changed that. I haven't looked into it yet this fall because we don't have as much access to the computers.
It has been a few years since I have used Edmodo, since my district has been pushing Blackboard. I did create quizzes for the students. If the questions were multiple choice, Edmodo would be able to grade it for you if you put in the correct response. Written answers had to be graded by the teacher.
Edmodo can be used as a forum where the students and teacher can have discussions. I also remember there was an option to create questions for students based on standards, which I really liked. I could use it to determine if students were advanced, proficient, or if the needed improvement with certain skills. I used this feature during my intervention class specifically.
Edmodo might have other features now since it has been a few years, but I really liked it and it was very student friendly. At the time I was teaching 5th grade and the students loved it!