To be honest: If it is really necessary to determine who’s superior to whom, I go by the regulations of the armed forces of the State I live in. As it happens, they suit a Federation Starship quite well, in my opinion. 
But, to be honest: Chain of Command and command authority shall be determined by consensus of the players. Star Trek is not military science-fiction in the first place and the game is not meant to be the simulation of a military. Every group should, in their session 0, talk about the chain of command and how it’s composed. If necessary, you can adjust the ranks, accordingly.
If you’re interested, on how the theory behind my reasoning about chain of command works, read on. But it’s just military theory that I stole from the real world. 
I will spare you the details, but, roughly, there are 5 (spoilered below: 6) cases that grant command authority over others.: Mission-Order > Speciality > Leadership > Department > Rank.
“>” indicates that command authority granted via the left weighs more than the authority granted via the right.
Mission-Order: If the command authority is ordered by a (common) superior, e.g. when the captain orders that a Lt is the leader of an away-team, even if a Cmdr is part of the away-team.
Specialty: The specialty job, e.g. military police, guards, security, etc. grants command authority, e.g. a Chief of the Security department can order a Lt of the Science department out of the brigg.
Leadership: This is the regular chain of command. The admiral of a fleet has command authority over all personnel within their fleet, the captain of a ship has command authority over all personnel aboard their ship, the deparment head… etc.
Department: This is an entirely different chain of command that relies on the profession. E.g. a doctor within Stafleet Medical has authority over how doctors on starships do their job. Most of the time, this has to do with regulations, but can also be relevant for direct orders.
Rank: Well, rank. A specialty here is that outranking someone does not automatically gives you command authority over them, but only in certain places and/or special times. This is something that is probably special to the armed forces of my home and may not be very intuitive for people used to other armed forces structures. Also, “outranking” is defined by groups of ranks, not the ranks itself.
Since, with the special rules under “rank” there are situations, where no officer has a command authority over one-another, there is a sixth rule:
Own Declaration: Officers and Non-commissioned Officers (but no Enlisted Personell) can declare themselves to have command authority over every person with a lower rank (not group, cf. above) than themselves, if necessary. Necessity is, roughly, defined with a state of emergency and/or lack of discipline.
To your examples: Data would have command authority over Crusher (and later Troi), because he is 2nd officer (either specialty or leadership in the list above; probably the latter). The ship’s chief medical officer has command authority over all personnel aboard (including the captain!) in all things medical, but limited to all things medical (that would be specialty in the list above).