You can't put photos and videos on icloud to save space on the device. What you should be doing is syncing these files to a computer for archiving. Once done, then you can delete the files from the device.
Read this... import photos to your computer...
I'd look to a 3rd-party app like dropbox or camera awesome and sign-up for a service to get past your short-term space issues. I know camera awesome (which uses smugmug) will let you upload photos directly from your phone, which you could then delete, and I believe it's also the case for dropbox.
I believe dropbox offers a certain amount of storage for free which should get you through the vaca.
1.) Flickr offers a ton of free storage, and you can upload from their app. Make sure that it will allow you to remove photos from your phone without also removing them from flickr.
2.) Delete a few apps you aren't using. Go to Settings, General, Usage, and it'll show you how much space each is consuming.