In the middle of the orgy, Megumi ran around the lawn stark naked.

Literal

Orgy [possessive-の] inside [at-で], Megumi [topic-は] stark-naked [with-で] lawn [object-を] ran-around.

乱交パーティー ('orgy party') combines the Sino-Japanese 乱交 with the loan パーティー. すっぱだか ('stark naked') is an emphatic form of 裸 — the すっ prefix intensifies. 走り回った ('ran around') is a compound verb (走る + 回る). The sentence is vivid narrative, probably from fiction, and demonstrates how Japanese handles explicit content with the same grammatical structures as any other sentence.