They all mean something similar, but could have slightly different shades of meaning. Keep calm means "don't get upset" or "do not show emotion", implying that while there is a reason to respond emotionally, a person should not allow emotions to overtake them. Calm down is an expression meaning "lower your emotional level". This is used when a person is already angry, and for one reason or another, needs to temper his/her emotions/behavior. Take it easy can be used in three ways-as a continuation of calmness, as a mild form of a command to lower your emotional level, or a warning to slow down. For an example in the first usage, if I am leaving my friends after spending a pleasant day with them, I would tell them all to "take it easy", meaning that I wish them all well and calmness as they continue in their day. However, if I am with a friend in an emotional situation, if I say "take it easy" it is to lower his anger (this command would only be used with the emotion of anger to reduce it). Lastly, if I have a friend who is overdoing something (such as moving down stairs too quickly, drinking too much, or moving too much after an injury), I would tell him/her to "take it easy" as a suggestion to slow down their current action. Hope this helps!

They are varities of sense.