1. "он не знает, с каким хреном редьку едят"
There is russian proverb "хрен редьки не слаще (horseradish is not sweeter than pungent radish)" (Note, there is difference in russian between редис and редька - both are radish in english, but редька is very pungent sorts of) meaning "both discussed alternatives are bad". So, this phrase is reference to "eating horseradish with pungent radish" = "taking both bad alternatives".
By the way, there is dirty rephrase of this proverb: "хер (compare with хрен) редьки не слаще" = "dick is not sweeter than pungent radish", grandfather of my friend of childhood liked to use it.
2. "завскладами цвели махровым цветом". зав-склад is "заведующий складом (chief of warehouse)". "цвести махровым цветом" is idiom "to prosper / to flourish" (literally "to flourish with big blossoms"). In soviet times deficit of goods was common thing and such professions had profits.
3. "отпаивать" here is not derived from "паять / to solder", but "поить / to give drink / water". "отпоить" is perfect form and "отпаивать" is imperfect form. "отпаивать" is process of giving some drink to somebody to bring him to life - in case of shock or something. "отпаивать водкой" - to give somebody vodka to relieve shock.
4. Again, unusual phrase, yes.