Learn Hardcore Icelandic: Hún er ennþá þreytt eftir ferðalagið.

Because the adjective agrees with the subject’s grammatical gender. Hún is feminine, so the predicate adjective is feminine singular nominative: þreytt. Other common forms:

Masculine singular: þreyttur
Feminine singular: þreytt
Neuter singular: þreytt (same spelling as fem.)
Plural: þreyttir (masc), þreyttar (fem), þreytt (neuter/mixed)

Where does ennþá go, and can it move?

In main clauses, Icelandic is verb‑second. The neutral place for adverbs like ennþá is after the finite verb and before the adjective: Hún er ennþá þreytt...
For emphasis you can front it: Ennþá er hún þreytt...
Placing it after the adjective (Hún er þreytt ennþá) can sound like an afterthought and is less neutral.

Can I use enn instead of ennþá?

Yes. Enn also means “still” and is fine here: Hún er enn þreytt... Many speakers find enn a bit more formal or bookish; ennþá is the everyday default.

How do I say “not yet” and “no longer” with this sentence?

Not yet: Hún er ekki ennþá þreytt or Hún er ekki þreytt ennþá. Both occur; the second often sounds a bit more natural in speech.
No longer/anymore: Hún er ekki lengur þreytt.
Note: ennþá = “still” (positive); with negation it’s “not yet,” while ekki lengur = “no longer.”

What case is ferðalagið in, and why?

Accusative singular (neuter, definite). With the temporal meaning “after,” eftir governs the accusative: eftir ferðalagið. The dative would be ferðalaginu, which is not used for the time meaning here.

Why is it ferðalagið (definite) — could I say ferðalag or use ferð instead?

Icelandic often uses the definite article when a specific, identifiable event is meant. Alternatives:

eftir ferðalagið = after the (specific) journey
eftir ferðina = after the (specific) trip (shorter, very common; ferð is the everyday word) For a general statement you’d go indefinite/plural: Hún er oft þreytt eftir ferðalög (“after trips” in general).

Can I use á eftir instead of eftir here?

No. á eftir means “later/afterwards” (relative to now) or “next/behind” and doesn’t take an object: e.g., Ég kem á eftir (“I’ll come later”). Your sentence needs eftir + object to mean “after the trip.”

Is eftir ferðalaginu (dative) ever correct?

Not with the time meaning “after.” eftir + dative occurs with other meanings (e.g., authorship/style: lag eftir Jón = “a song by Jón”). For “after [time/event],” use the accusative: eftir ferðalagið / eftir ferðina.

How would it change with different subjects (he/they)?

He: Hann er ennþá þreyttur eftir ferðalagið.
They (masc.): Þeir eru ennþá þreyttir eftir ferðalagið.
They (fem.): Þær eru ennþá þreyttar eftir ferðalagið.
They (neuter/mixed): Þau eru ennþá þreytt eftir ferðalagið.

Can I front the time phrase?

Yes: Eftir ferðalagið er hún ennþá þreytt. The verb stays in second position (verb‑second rule), and fronting adds emphasis to the timeframe.

How can I say “after having traveled” instead of using a noun?

Use a clause with eftir að hafa + [supine/participle]:

Hún er ennþá þreytt eftir að hafa ferðast. You can also say: ...eftir að hafa verið á ferðalagi.

Any quick pronunciation tips for tricky letters here?

ú (in Hún) is a long “oo” sound (as in “food,” but longer).
þ (in ennþá) is the voiceless “th” (as in “thin”).
ð (in ferðalagið) is the voiced “th” (as in “this”), often very soft.
The gi in -lagið often has a palatal glide, sounding a bit like a brief “y”: roughly “la‑y‑ið.”
Double nn in ennþá gives a slightly longer “n” before þ.

Does vegna work here instead of eftir?

Different meaning. vegna + genitive means “because of”:
Hún er ennþá þreytt vegna ferðalagsins = She is still tired because of the trip (focus on cause).
eftir ferðalagið = after the trip (focus on time).

What about ennþá vs enn þá (two words)?

Write ennþá (one word) for “still/yet.” enn þá as two words is rare and only used when enn (“still”) and þá (“then”) keep separate meanings in special contrasts. Stick with ennþá.