First off, I'm only just beginning to foray into the world of real bike components now. I've been a "toy" bike guy up until now, so bear with me.

I recently bought a new rear wheel for my 21spd Iron Horse Outlaw (the aforementioned toy bike) that I keep for a backup or loaner. Previously the rear wheel had a 7 sprocket freewheel equipped wheel which I destroyed. I replaced it with a wheel equipped with a freehub and 7 sprocket cassette.

The trouble I'm having is that now the derailleur system can't shift it all the way through the gears. It shifts from smallest to about halfway up the cassette, and of course indexing is all off. The derailleur is not hitting the stops, and I can pull the cable by hand, or push the derailleur manually, and it will shift all the way through. It's like the shifter does not have a large enough throw to accommodate the cassette, which I noticed after installation, is indeed wider than the original freewheel.

Is there a simple fix to this, or am I looking at more new components?

Bring it to your local bike shop and get them to look at it. It will be a quick fix for them.