Rāvaṇa threatens to eat Sītā for breakfast

Having killed Jaṭāyu, Rāvaṇa takes Sītā back to Laṅkā, but she refuses to become his wife. He threatens to torment her but she remains faithful to Rāma.

वृद्धम् खगम् हत्वा रावणः सीतया सह लङ्काम्  अगच्छत्

Having killed (the) old bird, Rāvaṇa went to Lanka with Sītā

वृद्धम् old, adj. agreeing with bird

खगम् bird. masc. accusative sing. Accusative because Rāvaṇa does something 'to' the bird. If it was just 'bird' in the nominative, it would have been खगः not खगम् . Please take special note of this. Not to distinguish between the two is a mistake very easily made by Hindi speakers. 

हत्वा having killed.This grammatical form is called the 'gerund'. It is an indeclinable (avyaya) particle. The ending could be  त्वा or य, and will not change with gender/number/case etc. It talks of an action that has already happened.

रावणः masc, nom, sing. 

सीतया सह instrumental case+ सह = 'with' Sītā

लङ्काम्  To Laṅkā. fem., acc., sing. 

अगच्छत् - went. 3rd person, nom., sing., agreeing with रावणः

लङ्कायाम् रावणः सीताम् पुनः अवदत् हे सीते मम भार्या भव इति

In Laṅkā Rāvaṇa said again to Sītā - become my wife.

लङ्कायाम् - in Laṅkā. locative, fem., sing.

रावणः - Rāvaṇa. masc., nom., sing.

सीताम्  - to Sītā. accusative, fem, singular

पुनः - again (avyaya)

अवदत् - said. Past tense of √वद् to speak

हे सीते - O Sītā. vocative, fem., sing. 

मम - my

भार्या  - wife nom., fem., sing.

भव - become. This is the imperative form of √भू to become

इति - direct speech marker, and an avyaya

सीता  तु न कदा अपि अवदत्

But Sītā said, never!

सीता fem., nom., sing.  

तु - but/lekin. avyaya - used for stress

न कदा अपि - never (once we do sandhi, you will normally see this as कदापि). कदापि means sometime, any time, but with the न it becomes NEVER

अवदत् - said

कुपितः रावणः सीताम् उद्याने अस्थापयत्

(The) angry Rāvaṇa placed Sītā in a garden.

कुपितः रावणः (The) angry Rāvaṇa - masc, nominative, singular. Note adj/noun agreement

सीताम् - सीता को fem, acc., sing. (again, please note it is not enough to say सीता as we do in Hindi. It has to be सीताम्) 

उद्याने in (a) garden. Locative, neuter, singular

अस्थापयत् - placed/established. past tense of √स्था 'to stand, stay

तस्मिन् उद्याने अशोकवृक्षाः आसन्

In that garden there were Aśoka trees

(I've always loved the irony of Aśoka w.r.t Sītā's state...)

तस्मिन् उद्याने - locative - in that garden 

अशोकवृक्षाः - Aśoka trees masc., nom., plural

आसन् - were. 3rd person, nom., plural past of √अस् - to be

रावणः अवदत् यदि  सीता अचिरेण मम भार्या न भविष्यति तर्हि अहम् ताम् प्रातराशे खादिष्यामि इति

Rāvaṇa said, if Sītā, does not become my wife soon, I will eat her for breakfast.

रावणः अवदत् - Rāvaṇa said

यदि  - if (avyaya)

सीता 

अचिरेण - soon (avyaya)

मम - my

भार्या - wife, fem., sing., nom.

न - not

भविष्यति - will become. 3rd person, sing., nom., future of √भू

तर्हि - then (we did yadi/tarhi on the 22nd of Sept)

अहम् - I

ताम्  - accusative, feminine, singular उस को

प्रातराशे - locative, masc., singular (lit. at breakfast)

खादिष्यामि - (I) will eat. 1st person sing., future of √खाद् to eat

इति - direct speech marker, and an avyaya

तत् श्रुत्वा सीता  अतीव दुःखिता अभवत् 

Having heard that, Sītā became very distressed/miserable.

तत् -that

श्रुत्वा - having heard - gerund, like हत्वा above

सीता  

अतीव दुःखिता extremely distressed - notice दुःखिता is an adjective and agrees with सीता, but अतीव does not, making it an ... avyaya

अभवत् - became, 3rd person, sing., past of √भू 

रावणः सीताम् राक्षसीनाम् मध्ये अस्थापयत् 

Rāvaṇa placed Sītā amongst demonesses

रावणः Rāvaṇa

सीताम् accusative fem., sing. सीता को

राक्षसीनाम् - genitive fem., plural - 'of' the demonesses 

मध्ये - in the middle. locative singular of मध्य (masc/neut)  

अस्थापयत् - placed/established 3rd person sing., past

राक्षसीभिः सीता पुनः पुनः पीडिता

Sītā was tormented again and again by the demonesses. (The 'asti' is assumed, which is very common in Sanksrit sentences. These are called nominative sentences) 

राक्षसीभिः instrumental, plural, fem., - 'by the' rākṣasīs 

सीता nom., fem., singular

पुनः पुनः again and again (double avyaya - 'baar baar')

पीडिता - tormented adjective agreeing with सीता 

राक्षस्यः पुनः पुनः आक्रोशन् रावणम् गच्छ तस्य भार्या भव च इति

The rākṣasīs shrieked again and again - Go to Rāvaṇa and become his wife.

राक्षस्यः - nom., fem., plural - rākṣasīs

पुनः पुनः - again and again

आक्रोशन् - (They) shrieked. 3rd person, fem., plural, past of √kruś 

रावणम् - masc., accusative., sing., to Rāvaṇa

गच्छ - go. imperative of √gam

तस्य - his

भार्या - wife

भव - become. imperative of √bhū

च - and (avyaya)

इति - direct speech marker (avyaya)

रामे एव स्निह्यामि इति सीता अचिन्तयत्

Sītā thought - I only love Rāma 

रामे locative case, (the act of loving takes the locative in Sanskrit)

एव - only (avyaya)

स्निह्यामि - I love  

इति - direct speech/thought marker (avyaya)

सीता - fem, nominative, singular

अचिन्तयत् - thought past of √चिन्त् - to think