Can I sacrifice an Ember Hauler during my opponent's turn?

As long as you can pay the cost and the rules for the ability allow you to (such as the equip ability and the loyalty abilities of planeswalkers which you can only activate on your turn), then you can activate them.

It is important to note that creature abilities are never cast so cannot be countered by things like cancel.

Absolutely. Unless there's some other restrictions to it.

602. Activating Activated Abilities


602.1b Some text after the colon of an activated ability states instructions that must be followed while activating that ability. Such text may state which players can activate that ability, may restrict when a player can activate the ability, or may define some aspect of the activation cost. This text is not part of the ability's effect. It functions at all times. If an activated ability has any activation instructions, they appear last, after the ability's effect.

602.1c An activated ability is the only kind of ability that can be activated. If an object or rule refers to activating an ability without specifying what kind, it must be referring to an activated ability.


602.2b The remainder of the process for activating an ability is identical to the process for casting a spell listed in rules 601.2b-h. Those rules apply to activating an ability just as they apply to casting a spell. An activated ability's analog to a spell's mana cost (as referenced in rule 601.2e) is its activation cost.

602.5. A player can't begin to activate an ability that's prohibited from being activated.

602.5a A creature's activated ability with the tap symbol ({T}) or the untap symbol ({Q}) in its activation cost can't be activated unless the creature has been under its controller's control since the start of his or her most recent turn. Ignore this rule for creatures with haste (see rule 702.10).

602.5b If an activated ability has a restriction on its use (for example, "Activate this ability only once each turn"), the restriction continues to apply to that object even if its controller changes.

602.5c If an object acquires an activated ability with a restriction on its use from another object, that restriction applies only to that ability as acquired from that object. It doesn't apply to other, identically worded abilities.

602.5d Activated abilities that read "Activate this ability only any time you could cast a sorcery" mean the player must follow the timing rules for casting a sorcery spell, though the ability isn't actually a sorcery. The player doesn't actually need to have a sorcery card that he or she could cast.

602.5e Activated abilities that read "Activate this ability only any time you could cast an instant" mean the player must follow the timing rules for casting an instant spell, though the ability isn't actually an instant. The player doesn't actually need to have an instant card that he or she could cast.

Yes you can

yes, all abilities are instant speed (meaning you can activate them anytime you have priority) unless they said otherwise.