There's no such thing as a "strained knee" as a medical diagnosis - it's a complicated structure, and what you actually strain are the various ligaments and tendons that suppport the joint. The symptoms you get will depend on which bit has been strained, how it was damaged, how badly it's been damaged etc. Knees are notoriously difficult to diagnose, however, and sometimes "strained knee" may be the best you can do without MRI, arthroscopy etc.
Symptoms of a knee injury include swelling of the knee joint, pain on various movements, warmth and possibly reddening, possibly some instabiity if the ligaments have been badly damaged. The knee may also lock in a certain position if the cartiilage has been torn in a particular way.