The recommended method to import MSG files into your Outlook account is to first convert them into a PST file format and then import the newly created PST file. The Softaken MSG to PST Converter is capable of converting either single or multiple MSG files into one single PST file with all email content (including attachments) and format being preserved. Following the conversion of your MSG files to PST, you will simply open your Outlook application and select the Import option to import your newly created PST file.
This software will work simply and efficiently and will allow for the importing of multiple MSG files at the same time. There is a trial version for you to download and evaluate prior to purchasing.