If the files do not fit you will need to work out how to stream them - that will depend on where the files came from & if you have reliable hosting & fast internet etc.
I assume you have the files in iTunes on a computer, if that is the case consider enabling the option to sync SD movies (set in the 'Summary' options when syncing). If you are lucky these files will contain a HD & SD version that can allow them to sync. The App store may have the option to download SD versions if these are purchased there, try looking in your purchase history for that if the Files are HD. Get Info on each file to examine that.
Otherwise try selecting the files in the iTunes TV Shows list & attempt to create a new version via the 'File menu > Create iPhone/ iPod version'. It may reduce the size sufficiently to cram them onto the device.
iTunes store purchases cannot be converted due to the DRM.
Also consider removing apps & other files to make room, assuming they are less important compared to the videos.
iOS lists the storage used under the 'Settings app > General > Usage > Manage storage', see if that gives you ideas what to clear out.
P.S. I believe the 'Camera Connection Kit' can play movies stored on SD cards, but I have not experienced that - it may only work with non iTunes store purchases (gotta love DRM). Search here for note, I'm sure others have discussed this. It may be a way to workaround it?