moving into a new apartment. There is a used refrigerator, stove and dishwasher. Management will not replace it without raising my overall rent. Can these items be kashered?
For the fridge, no special kashering is required, other than thorough cleaning. It is preferable to pour hot water onto the shelves from a kettle, in case there were spillages of hot foods.
The dishwasher can be kashered by first ensuring that it is entirely clean, including spilling bleach or similar cleaning substance into cracks and crevices that might not be reached by water. The dishwasher should then be activated at maximal heat, for a full cycle.
For the stove, the grates requires libun kal, which can be achived by heating them on the fire to the degree that paper touching them would burn. For the rest of the stovetop, boiling water must be poured onto the stovetop, preferably in combination with an even melubenes, a heated brick or stone (or other substance) that is moved across the surface.
For the stove, see Rema, Yoreh De’ah 92:8; Rema, Orach Chaim 451:4, and Mishnah Berurah 451:32.
For the dishwasher: According to most authorities, one can do hag’alah for plastic (see Iggros Moshe 2:92; Chelkas Yaakov 2:160). In addition, the dishwasher is usually used with substances that are pagum, and therefore the initial belios are not clearly issur. See also Mibeis Levi (Nissan 5756, p. 36), who writes that the dishwasher should not be kashered for Pesach, yet hints that this can in principle be done. In this case, where not kashering will involve a significant loss, one can be lenient, by means of the procedure above.