Is it normal for a group of this size not to have source control?
In my experience, it is not the norm, but not as completely unusual as other answers here suggest. The majority of small companies does use source control, but a significant number doesn't, unfortunately.
I have so far been given only vague reasons for not having source control - what reasons would you suggest could be valid for not implementing source control, given the information above?
See this question on SO for a good discussion. The accepted answer says:
"There are no good reasons not to use version control. Not one."
Are there any more reasons for source control that I could add to my arsenal?
The consensus among all developers and project managers I have met, and of course here on Programmers and SO is that source control is a must. It's an accepted best practice. If somebody decides to ignore it, he needs to have some very strong and convincing arguments why this is the right decision for him (i.e. a little more than 'we never needed it, so why should we need it in the future'). The arguments you have presented so far are focused on specific issues, perhaps you should try a wider approach along the lines of 'everybody does it, so why don't we as well?