Since you're a command-line user, you can use ffmpeg to do the conversion for you. I suspect when you mount your Sony camera, it probably always gets the same volume name. (Probably something like /Volumes/SONY/ or /Volumes/DSC/ or something like that.) You could write a script that basically walks through the directory containing the movies, and converts them to a suitable format, saving them on your hard drive.
Looking at iTunes in Automator.app, I see that it supports an "Import Files Into iTunes" function. You could probably make an Automator action that calls your ffmpeg script, then imports the results into iTunes. From there, you just sync your iPhone. (Not sure if it will auto-sync large videos via iCloud or not, but it might.)
I'm not the best at scripting or Automator, but you can probably get an answer to the specifics on either Ask Different or Super User.