Moving iPhoto and iMovie libraries
Yes, it is possible to just close the libraries and move them to an external HD. This will take long time to copy across (leave it overnight) but will work.

Moving them to an offsite solution is not supported by iPhotos/Photos/iMovie and so your mileage may vary. There are some third party software solutions that can help with the management of large libraries. Bear in mind that something cloud-based will be very much slower to access unless it also uses local disk space - which was what you were trying to avoid. It's great for offsite backup, but not for browsing, editing, etc.

After you've moved to the external hard drive, if you then run iPhoto/Photos while holding the ALT/option key, you can choose to create a new library to start fresh. We do this on Jan 1 each year and put the whole year of photos and videos in one library so that it keeps to a manageable size.