Well, you don't /have/ to RP a power use every time. I've only ever known one gamer who actually chanted words of power when his character cast a spell, for instance.
But, if the situation is ripe for it, it's fun, and it can differentiate your warlord a bit. If you're the drill seargent type, you can shout some insults, if you're the noble knight you can make a 'St. Crispin's Day' speach.
I RP some of my powers, and use it to highlight my relationship with the other characters, or play to thier character concepts a little. Our rogue is my warlord's childhood friend, and bit of a jerk, so throw in a little good natured ribbing. The party defenders, OTOH, are actual soldiers under my command, so I'm more likely to shout orders to them - making that a little more interesting is that one of them takes orders in a different language, Deep Speach, and, because the player is a major otaku, Japanese stands in for Deep Speach. That's actually kinda fun, because he really does speak japanese, so when I read a word or phrase off my note card, he generally gets it better than if I say the name of the power.
Often, though, I don't actually RP it. There are only so many powers a 4e character gets, and after a while, Inspiring Word is just inspiring word, and it doesn't really add much to try to come up with a new cool thing to say every time.
We generally treat other classes' powers the same way. Sometimes the fighter describes the move or the DM describes the effect on the victim in detail, but often it's enough to get through his turn and figure out which exploit, whether he hit and how much damage was dealt.