I just looked at all five and they all look like they're stuck in the same spot: very powerful effects, but not powerful enough to bother using with something that circumvents mana cost. And unfortunately, they're not viable with the mana costs they have. Triple mana of one color is pretty prohibitive as it is. double mana in two other colors for a total of seven is ridiculous. Players will generally find it easier to hardcast stuff like Polar Kraken than any of these cards. For example, Brilliant Ultimatum replaces Polar Kraken's "8" with "WWBB" and this on top of the UUU already involved in both. And the effect is good. It's like Fact or Fiction on steroids, but Fact or Fiction, while a great card, isn't so great that being able to play the cards for free is worth making the cost so impossible.
Any of them is potentially viable in casual decks, but not the sort of thing you'd build a deck around. More like something that could hit during the late game and change things drastically. They could be good in 150-card highlander if people still play that.
Brilliant Ultimatum: This becomes increasingly powerful with the number of bombs sitting in your library. But bombs are expensive and so is this. So it's an extremely expensive card that is best used when you're playing a bunch of extremely expensive cards. I'd rather Fact or Fiction and hardcast what I get or just Mind's Desire and win, which is still more feasible than casting this.
Clarion Ultimatum: I can't really think of an instance in which this card would be particularly awesome. It just might be the dud of the cycle, which is saying a lot, since these cards are all kind of bad. Reminds me of Assembly Hall, a card I somehow acquired a playset of and wanted to use, but couldn't break because it was totally a crap rare. There simply isn't some combination of five permanents that one might have out that, when an additional copy of each is fetched from the library, becomes a winning combination where it wasn't before. And if there were, WWWUUGG would be too expensive anyway.
Cruel Ultimatum: At least this one's pretty cool. It could potentially be played in a long, drawn out match and hit the opponent in three places (at least one of them is going to matter) while helping you in three places. But if you want to actually be efficient, using a card that just does one thing and is actually affordable would be a lot better. This is a mere gimmick.
Titanic Ultimatum: Reminds me of Vitalizing Wind. But Vitalizing Wind didn't have the intimidating color requirements of this thing. Overrun is better than either anyway. If you have enough creatures out, this does win the game and it might be the best of the five, but Overrun is a much more viable option and even Vitalizing Wind seems better.
Violent Ultimatum: Might be the most affordable because of the B/G combination, two colors that allow for more mana production and mana-fixing than others generally. But it's a bit too situational. I'll take Pernicious Deed over this any day.