As long as you are not blacked out you can watch all the games with at bat/mlb.tv. I got extra innings via my cable provider a few years ago and there were far fewer games available to me when I did that. They only had like 10 channels so if several games were going on at the same time you had to hope the Royals game was going to be on one of those. With at bat every Royals game will be shown even when the Royals network isn't carrying it, the other market will and you can watch that one instead.
You can listen to Royals radio network on at bat as well as watch the tv of the home or away so long as you are not in the blackout area. If you live in chicago you're going to be blacked out of every game the Cubs and White Sox play so when the Sox are playing the Royals you'll only be able to listen to the audio.
I love my mlb.tv/at bat.
As far as radio links
http://tunein.com/radio/stations/Kan...Royals-a37924/ I haven't tried this in a while but I used to use this before I just got the package. Most of the links aren't going to work because they're not supposed to carry them, but generally there is one or two every day that forget to shut off the feed.