You could ship the MS dlls near your exe, I'm not sure if it's legal though.
As for installer: you can try NSIS, some commercial solution or making your own (in Qt, LCL, GTK+, FLTK, etc. probably not recommended unless you want to have the bragging rights and extra fun).
I personally prefer simple 100% self contained zip files (not even these self extracting ones, 100% plain zip files) but an installer can have some advantages I guess (installing dependencies, setting stuff up, finding user home dir to save stuff and configs to, etc).
As for OpenAL and other LGPL stuff, the agreed upon way seems to be: use a dll and say in a README or somewhere that you use LGPL licensed lib named so and so.
https://softwareengineering.stackexchange.com/a/86158In theory a source code link, copy or a point of contact to request a copy is required* and full license text should be included but.. many people skip that and the authors don't seem to ever care. Due to problems with GPL, LGPL, etc. people seem to follow them in the spirit only, unless someone does something really crazy and even then the first action is a polite reminder, not instant fucktillion dollars lawsuit/DMCA equivalent/whatever since that'd be a huge gift to enemies of FOSS and an image suicide for the authors of the library and the library itself.
* Or something like that. There are tons of edge cases and people online, interpretations of the license text, opinions of library authors, FAQs on FSF and so on all seem to argue and disagree what is required exactly.