How do plants get their O₂ for respiration during the night?
Not all plants have their stomata closed during the night. A notable exception are Crassulacean acid metabolism(CAM) plants that keep their stomata closed during the day and open it during the night. This is a common evolutionary strategy with Xerophytes.

There are also 2 other types of metabolic pathways namely C3 and C4. As a consequence we get what is called a C3 and C4 plant, which aptly represent the predominant metabolic pathway it employs.

Additionally plant cells, like all life, can produce energy without oxygen by Glycolysis. Furthermore, when stomata is closed, oxygen respiration is restricted, not blocked entirely. Finally it might be important to note that plant metabolism is reduced during the night.

Full disclosure, I am not a botanist. Please let me know if there are any glaring errors.