ごみわべつのふくろにいれます(Gomi wa betsu no fukuro ni iremasu)
べつのふくろにごみおいれます (Betsu no fukuro ni gomi o iremasu)
ごみおべつのふくろにいれます(Gomi o betsu no fukuro ni iremasu)
Which if not all, is appropriate?
All of these sentences are grammatically almost correct, but you should use を instead of お for the particle o, and you should use は instead of わ for the particle wa.
Here are the corrected sentences:
Sentence 1 uses the topic marker wa instead of o, and the sentence sounds like you're describing some general things about garbage. The sentence can be typically used when you're explaining to someone how to separate waste in your town. "I/You/etc (always have to) put garbage into a different bag."
Sentences 2 and 3 are almost the same, but what comes first tends to be focused more strongly. Typically, these sentences can be used when you are describing what you have to do now: "I (will / am expected to) put (this) garbage into a different bag (now)."
Good points from naruto. I'll try to add some thoughts on why using topic-marker 'wa' is even possible.
'Wo' marks the direct object in the sentence. So the most vanilla way of saying "I put the garbage in a different bag" is:
This is the no-frills, plain-Jane version of this sentence.
To go to the next step, we need to review that Japanese has the really cool property of not requiring objects to be explicitly present if they are already understood. So the sentence
is also totally correct, and means "I put it in a different bag." Notice that in the English, we have demoted our direct object to the placeholder word "it." It's still there, but just barely. In English, we have to keep a placeholder because word order is very important. However, in Japanese, the direct object can simply be eliminated.
The particle 'wa' marks a topic, and that topic is really kind of off in its own world. It doesn't really directly contribute to the subject-object-verb main structure of the sentence. It merely offers a topic for consideration.
So we can understand the 'wa' sentence to work more like this:
Structurally, you can understand this as being extremely similar to the English "Now when it comes to the garbage...I put it in a different bag."
Notice that the direct object of this English sentence is actually still the placeholder word "it," not "garbage." What did we put in the bag? It. We put it. What's it? Well, the speaker took pains to direct our attention to the topic of garbage, so that's what it must be.
This is precisely what is happening in the Japanese.
Why would a person structure the sentence this way when you could just explicitly mark the object with 'wo'? As naruto points out, this is a pattern used for certain kinds of explaining. You can kind of feel something similar in our English examples. If you say, "Now when it comes to the garbage, I put it in a different bag," it sounds like you're explaining some kind of general principal, or perhaps you're trying to draw a distinction from some other bagged items. ("The compost, I put here, but as for the garbage, I put it here.") At any rate, something special is going on, something that that the speaker wants to draw our attention to in a way that is different from a plain vanilla "I put the garbage in a different bag."
Hope that helps!