Metaphor in Crime and Punishment
This idiomatic phrase refers to a job, client, or anything that brings in a steady income. Nastasya tells Raskolnikov that he shouldn't make excuses to not tutor students because it's his sole means of earning money at the moment.
This is another example of Razumihin choosing more playful vocabulary to describe his friend Tolsyakov. Here he uses "bird's nest" to refer to his friend's hair, which described in this way gives the impression that it's rather unkempt and possibly dirty.
Razumihin is having a little linguistic fun with a metaphor for a friend's hat. He calls Tolstyakov's hat a "pudding basin," which is an earthenware or glass bowl used to steam puddings.
"Treacle" is another word for molasses, a kind of sweet, uncrystallized syrup. Money is not sweet, and so this comparison is helping to show how dear or precious money is to the men, and how badly they need money.
This is a rather obscure line in translation and in the original Russian, which says "Practicality walks about in boots" (Деловитость в сапогах ходит). Regardless of the actual meaning, it does appear that Razumihin is using this slang expression to emphasize his point that there's no practicality.
Dostoevsky uses this expression to remind the readers of how small and cramped Raskolnikov's garret is. Since the space is very small for only one person, it is very crowded in this moment, and Luzhin has to squeeze his way into the room to find a place to sit.
Katerina Ivanovna uses an interesting and ironic metaphor for her life. A ball refers to a very fancy party, often associated with aristocrats and high-class persons. Her life after her youth was far from this, and given what we know about her weakened psyche, it's unclear whether she is being ironic or somewhat sincere.
Since a "gutter" is a low play on a roof or street designed to carry off rainwater, using this word to describe children indicates that they are very low on the social ladder, possibly orphans.