atarasii sakusen no okage de sigoto no kouritu ga agarimasita.

おかげで is a fixed pattern meaning “thanks to” or “as a result of (in a positive sense).”
• You attach の to a noun (or noun phrase) and then で.
• It introduces a positive cause or reason for something good happening.
• Example: 天気のおかげで “thanks to the weather…”

Grammatically yes, but semantically no.
• おかげで conveys a positive result.
• せいで also means “because of,” but carries a negative nuance (“unfortunately,” “due to someone’s fault”).
Using せいで here would sound like you’re blaming the new strategy for some negative outcome.

上がる is an intransitive verb meaning “to rise, to increase.”
• Intransitive verbs take が for their subject (the thing that rises).
• You wouldn’t use を (that’s for direct objects).
• You could use は for contrast or topic, but が is natural when introducing or emphasizing that “efficiency” is what went up.

• 上がる means “to rise.”
• The past polite form 上がりました indicates the action is completed and adds politeness.
• If you wanted plain speech you could say 上がった, or if you want to describe an ongoing general fact you might use 上がる.

The の links 仕事 (“work”) to 効率 (“efficiency”), forming “efficiency of work.”
Without 仕事の, 効率 would be generic—you’d need the modifier to specify whose or what efficiency.

Yes. For example:
• 新しい作戦のおかげで、仕事の効率が上がりました。 (same)
• 新しい作戦によって仕事の効率が向上しました。 (using によって + 向上する)
• 新しい作戦が功を奏し、仕事の効率が上がりました。 (using 功を奏す “to be effective”)
All convey that “the new strategy improved work efficiency.”