The themes size videos for the maximum width of the post or page area by default which means you are going to have to resize them.
To get them side-by-side, the best way is to use an HTML table (3 columns) and then insert the videos into the cells of the table. Since the wordpress editor does not have a table function, you will either have to hand code the HTML, or use one of the online HTML table creators. This is one I've used before and it works well: http://www.quackit.com/html/html_table_generator.cfm . After creating the table, you copy all the code and then insert it into the post in the HTML tab.
You will have to do some playing around with the video widths to get them and the table to fit in the post/page area without breaking the theme. If the table is too wide for the available area, it will break the theme.
Getting them to enlarge by clicking on them I don't think is possible, and the video is going to be so small that I don't think they will be able to select the full-screen mode - if the video player has that feature.