Question

The poet draws an analogy between an old clock and a monk in these lines from a poem. Which phrase is analogous to "its case of massive oak"?
Halfway up the stairs it stands,
And points and beckons with its hands
From its case of massive oak,
Like a monk, who, under his cloak,
Crosses himself, and sighs, alas!
With sorrowful voice to all who pass,—
(from "The Old Clock on the Stairs" by Henry Wadsworth Longfellow)
sorrowful voice
its hands
crosses himself
his cloak

Answer 1

So, the massive oak refers to the case of the clock, that is, to the outside cover of the clock.
The outside cover of the monk is the cloak, and actually, we see the comparison directly here:

From its case of massive oak,
Like a monk, who, under his cloak,

So the answer is his cloak!