Okay, the answer is probably no, but I would like it to be yes:

Suppose I have Nova Blast on a character with Pulse Wave and Damage 3 or greater, and they blast away on a group of opposing characters, would they do their damage to applicable terrain features as well (objects, walls, blocking terrain, etc.)?

Concievably it makes sense, when someone goes 'nova' indoors like whatshisface at the beginning of Civil War and blows up an entire house. And it seems that if you can lay 4 clicks on Juggernaut and Green Scar you should be bringing down a wall too with the same attack. But I don't think the game mechanics support this conclusion as Pulse Wave only mentions damaging characters and Nova Blast does not add anything to how PW effects, or is affected by, terrain.

Just want to be sure on this one before I dismiss it completely as illegal.
Thanks!

Pulse Wave draws lines of fire to every character within the character's halved range. Unfortunately object are objects and not characters and thus would not be damaged.

Somethings you may want to keep in mind when using Pulse Wave are:
1. Pulse Wave ignores powers, feats and team abilites, not terrain feats such as hindering terrain. So any character that occupies hindering terrain gets the plus one to their defence value.
2. If using Pulse Wave using the Endurance feat saves you from the two pushing clicks you would recieve.

Mahazulu is right.

He blew up a little more than one house though, it was more like a city block or something around that.

Adding to mahazulu's post, if your character has indomitable, he doesnt take the pushing damage associated w/ nova blast.

Only temporarily. The Endurance is likely to bite you sooner or later.

And it will bite you with both clicks because you put one token on Endurance for each click ignored. In the case of Nova Blast, you ignore 2 and put 2 tokens on the card.

Hindering terrain does not give the +1 bonus on defense when a character is using Pulse Wave. The reason why characters don't get the +1 bonus in hindering, is because: "Attacks made by this power do not target characters".
It's the line of fire that is affected by terrain, meaning Pulse Wave can't shoot through blocking or elevated terrain.

Thanks guys. I figured it was not allowed. Thanks for the suggestions!

This is so wrong. All terrain effects apply normally to a Pulse Wave attack, including the hindering terrain bonus.

Absolutely wrong. Terrain affects Pulse Wave like normal. Blocking terrain blocks it like normal and hindering terrain grants the bonus.

EDIT: Quebbster already broke it down. Sorry.

I would'nt be so sure about the + 1 bonus on defense, if I were you: Pulse Wave doesn't TARGET any characters, the user of the power isn't aiming the normal way but rather "exploding" in every direction (that's how I see it).

I would. Directly from the PAC: "...lines of fire ignore characters, but are affected normally by terrain." Hindering terrain gives a +1 to the defense of any figure occupying it when being attacked from range (with the exception of the usage of some TA's and feats).

Actually the way I see it, if this helps, is it does target every character in its blast radius. Everyone that is in range of the blast is targeted, so they still get the +1 defense from terrain, the blast just ignores everything else.

Its also in the rulebook as pointed out above.