Currently I'm distributing a software product that includes three merge modules:
Microsoft_VC80_CRT_x86.msm
ATL.msm
policy_8_0_Microsoft_VC80_ATL_x86.msm
Some customers use packaging technology that doesn't like these MSM files (I think because they have technical problems with them writing to WinSxS). Can I just distribute the dll files directly into my application's Program Files folder, and if so which dlls do I need? Is it just atl80.dll?
Your alternative is to run the VC_redist.exe for that version of Visual Studio, run it from the bootstrapper with whatever setup tool you're using.
I don't know what you mean about packaging technology. The only way merge modules (msm files) can be installed is to add them at build time to an MSI file build. In other words, the only packaging technology that's relevant is Windows Installer and MSI files. So you need to find out exactly what this issue is. Everyone uses the merge modules or the VC_redist.exe because it's the only reliable thing to do.
One issue with doing it yourself in an unofficial way is that Windows Update can't find them (and that applies to static linking to). So when Microsoft applies a security fix to those Dlls then you are leaving your customers vulnerable.