This may have been discussed somewhere, but I can't find it. So I brought it up.
If I happened to use Godsend vs any creature and exile it, and my other opponents have the same creature that was exiled, can they cast it? As per the 3rd ability of that particular existence of that Godsend.
Example, blocking an Omnath, Locus of Rage. One is the Commander, the other just a creature. Exile the creature, can the commander still be cast?
Godsend's third line states "Opponents", plural. So no your other opponents will not be able to cast cards that have the same name as cards exiled by Godsend.
If you control Godsend and a card is exiled with it, each of your opponents can't cast spells with the same name as that card (no matter who owns those spells) (C.R. 108.1). For example, if a card exiled with Godsend this way is Grizzly Bears, your opponents can't cast spells named Grizzly Bears (whether they own them or not).
However, if a commander is exiled this way and the choice is made to move that commander out of exile to the command zone (C.R. 903.9a), that commander won't count as a "card exiled with Godsend" anymore for the purposes of Godsend (since that commander isn't in exile anymore) (C.R. 607.2a). See also this thread.
EDIT (Dec. 30): Edited.
EDIT (Jul. 2, 2020): Edited to conform to rule update with Core Set 2021; the rules changed so that a commander that's exiled doesn't necessarily go to the command zone immediately.
All of your opponents are, well, opponents, so they can't cast a creature with the same name as an exiled card no matter who owns the exiled card. That means if one Angry Omnath that isn't a commander gets exiled by this effect, the owner of one that's a commander can't cast it from the command zone or anywhere else as long as Godsend is still around.
However, the owner of a commander will probably elect to have it go into the command zone instead of exile, so keep that in mind.
@peteroupc, if a non-commander creature is exiled by Godsend and another player happens to be using that creature as their commander, that player will not be able to then cast their commander, correct?
Say player A has Omnath in their deck and they play it. I send in a creature equipped with Godsend, player A uses Omnath to block and it gets exiled.
Now player C has Omnath as their commander, they're just TSOL as they will not be able to cast their commander until Godsend is destroyed.
@peteroupc, if a non-commander creature is exiled by Godsend and another player happens to be using that creature as their commander, that player will not be able to then cast their commander, correct?
Say player A has Omnath in their deck and they play it. I send in a creature equipped with Godsend, player A uses Omnath to block and it gets exiled.
Now player C has Omnath as their commander, they're just TSOL as they will not be able to cast their commander until Godsend is destroyed.
If one Omnath, Locus of Rage (whether it's a commander or not) is exiled with Godsend, no opponent of Godsend's controller can cast a spell named Omnath, Locus of Rage, whether it's their commander or not and whether or not they own that spell or the exiled card (C.R. 109.5, 108.1). This lasts while Godsend remains on the battlefield and the Omnath moved to exile this way stays in exile (C.R. 611.3b, 607.2a).
If I happened to use Godsend vs any creature and exile it, and my other opponents have the same creature that was exiled, can they cast it? As per the 3rd ability of that particular existence of that Godsend.
Example, blocking an Omnath, Locus of Rage. One is the Commander, the other just a creature. Exile the creature, can the commander still be cast?
However, if a commander is exiled this way and the choice is made to move that commander out of exile to the command zone (C.R. 903.9a), that commander won't count as a "card exiled with Godsend" anymore for the purposes of Godsend (since that commander isn't in exile anymore) (C.R. 607.2a). See also this thread.
EDIT (Dec. 30): Edited.
EDIT (Jul. 2, 2020): Edited to conform to rule update with Core Set 2021; the rules changed so that a commander that's exiled doesn't necessarily go to the command zone immediately.
However, the owner of a commander will probably elect to have it go into the command zone instead of exile, so keep that in mind.
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Say player A has Omnath in their deck and they play it. I send in a creature equipped with Godsend, player A uses Omnath to block and it gets exiled.
Now player C has Omnath as their commander, they're just TSOL as they will not be able to cast their commander until Godsend is destroyed.