Most people don't pay as much attention to rhythm guitar as they should. A song usually consists of more rhythm than lead so you should be proficient at rhythm to write and play great songs. Let's forget about our scales for a second and concentrate on rhythm.
Rhythm guitar has a close relation to drums; you often have to think like a drummer to create unique strumming patterns. Listen to the drummer as you play. There are many parts drummers play that you can accent in your strumming. You can accent on the bass and snare drums, the high hat, or even follow a drum fill. In the end remember that you have to give the music space so don't try to fill every place in the rhythm up with strumming, it will just sound busy. You must work together as a band to create a cool rhythm groove.
Try variations of down, down-up, up-down, and up strums and make a distinctive pattern that repeats so that a listener can start to feel the rhythm pattern.
As far as feeling stiff and problems with faster rhythms, this usually has to do with tightening up your arm or not using your full arm while strumming. Contrary to speed picking with rhythm you should use you arm to help create the rhythm feel.
DO NOT TIGHTEN UP YOUR ARM!!! Let your arm be relaxed and loose and really try to feel the rhythm.
As you progress you will start to get your own signature strumming patterns and it will be easier for you to show your own identity.
Remember that rhythm is vital to make great songs--so strum away!!!!