How does Achebe vividly convey Obi's feelings towards Nigeria in No Longer at Ease?
The answer to your question is that Achebe uses both diction (word choice) and characterization (both indirect and direct) to convey Obi's feelings about Nigeria in No Longer at Ease.
At the beginning of the novel, Obi is enamored with his homeland and speaks about it very idealistically. The best example of this is Obi's own words within his poetry. Through Obi's own words (and Achebe's use of diction here) the reader learns about Obi's feelings quite vividly. This is Achebe's use of indirect characterization in that the narrator does not tell us directly about Achebe's feelings; instead, we learn about these feelings of idealism through Obi's own poetic words. Achebe also uses direct characterization to convey Obi's vivid idealism. There are times when Achebe tells us directly how Obi is feeling.
Obi [longed] to be back in Umuofia. This feeling was sometimes so strong that he found himself feeling ashamed of studying English for his degree.
In this use of direct characterization, Achebe shows that Obi's feelings for his native Nigeria are vivid.
Later in the novel, Obi is discouraged with Nigeria. Obi now knows that escaping corruption seems to be impossible for a public official. We learn this through Obi's actions. In short, Obi begins to accept bribes (a practice he was vehemently against earlier in the novel). Due to these actions (and the use of Achebe's indirect characterization), the reader discovers that Obi's feelings have changed about Nigeria. Obi's vivid feelings of discouragement are also shown through his own words against idealism:
The impatient idealist says: "Give me a place to stand and I shall move the earth." But such a place does not exist. We all have to stand on the earth itself and go with her at her pace.
In yet another piece of indirect characterization, Obi shows his discouragement with Nigeria by admitting that idealism "does not exist." Unfortunately for Obi, going "with [the earth] at her own pace" now means accepting bribes.