earthen slop jar a large-mouthed, enameled container used indoors at night as a toilet.
citified straw hat The reference is to a straw hat worn for purely decorative reasons. Eva might have been able to forgive BoyBoy for having left her with three children to support, but his overly pompous return as a pretentious, quasi-sophisticated "citified" person makes her finally feel inferior enough to be able to hate him thoroughly.
a cat's-head stickpin In southern culinary slang, a cat's-head is a big lumpy biscuit, so BoyBoy's stickpin would probably be large and ostentatious, in bad taste.
the Courier The reference is to the Pittsburgh Courier, one of the most widely circulated black newspapers at that time.
Garret . . . Buttercup brand names of oleomargarine, a substitute for real butter.
bent spoon black from steady cooking Plum is addicted to heroin; he buys it in solid form and places it on a spoon, which he then puts over a fire in order to melt it into a liquid. Because addicts are usually too shaky to hold the spoon with a pair of pliers until the heroin is liquid and ready for injection, they bend back the spoon handle like a Christmas tree ornament hook and then slip it over the side of a pan in order to keep the spoon steady.
dip-down walk a swagger-like gait, lifting the heels high and rocking for a split second on the balls of the feet before taking the next step; the walk was created by young black males in order to appear sexy and attractive to young women.
Liberty magazine a popular magazine of the 1920s and '30s.
