Can to you have a slight injury to the chest and still get a pleural effusion or pulmonary edema

Not really : what is your definition of slight injury? If we are talking trauma, like a blow to the chest, then you would more likely see a pulmonary contusion or maybe a lung collapse than effusion or edema. Those two things describe fluid around the lung (effusion) or waterlogged lung tissue, like a sponge in the case of edema. The mechanisms for these are not usually related to trauma or injury per se