Torment of Hailfire's effect means: "Repeat the following process X times. Each opponent may sacrifice a nonland permanent or discard a card. If they don't, that player loses 3 life." (C.R. 117.12a; see also C.R. 117.12). Thus, at each iteration, if an opponent (of that spell's controller [see also C.R. 109.5]) can't discard any cards, they can still choose to sacrifice a nonland permanent if possible (C.R. 608.2d). If they sacrifice one this way, they won't lose 3 life. (Note that under C.R. 608.2d, that player can't choose an impossible option; for example, to discard a card when they can't do so.) See also this thread and this thread.
For Death Cloud, any part of the effect that can't be done is ignored (C.R. 101.3, 609.3). For example, when Death Cloud resolves—
if one or more players can't discard any cards, as many players as possible discard X cards, to the extent possible (C.R. 101.3, 609.3), and
if one or more players can't sacrifice any creatures, as many players as possible each sacrifice X creatures, to the extent possible (C.R. 101.3, 609.3).
The word "unless" makes me think that I'd be losing 3 per x because I'm not fulfilling the other part of the requirement.
(W/U)(B/R)GForm of Progenitus, Shape of a Scrubland
BRGJund Tokens with Prossh, the Magic Dragon Foil
URGAnimar, the RUG CleanerFoil
RRRFeldon of the Third Path 2.0 Foil
BG(B/G)Not Another Meren DeckFoil
UR(U/R)Mizzix, Y Control and X Burn Spells
(W/U)(B/R)GHarold Ramos - The 35 Foot Long Twinkie (In +1/+1 counters)
UB(U/B)Dragonlord Silumgar
For Death Cloud, any part of the effect that can't be done is ignored (C.R. 101.3, 609.3). For example, when Death Cloud resolves—
EDIT (May 14; Dec. 28): Clarification.