I've looked around the AppStore for this but have not found one yet. Maybe my keywords are all messed up. Is there an app that will allow me to read files created by Microsoft Office on the iOS?
Microsoft has an official OneNote for iOS on the App Store. It was free for a limited time when I got it. It is still buggy, but should get better as it is the official app. As far as the other Office file types, I know of an app called Documents To Go. I cannot officially recommend it since I do not own it. I just know it's out there and that it supposedly allows you to open and edit Office files. You may want to check it out.
I do agree with David's answer in that if you just need to open these files, Dropbox is a very decent solution. I use Dropbox to open files I create at home using Pages and Numbers (I do not use Office, but if I did I would still use Dropbox to open the files I had created on my iPhone). Dropbox will not allow you to edit the files, but to quickly open while on-the-go it is a very good solution. Good luck.
These can be displayed by IOS with no software involved, other than OneNote. The trick is getting the files onto the device. Email is one way; you can view these files, other than OneNote, as attachments, using the ioS Mail app.
Another alternative is to use a sync service client (e.g. dropbox) to access the files.