Is there no way for me to play the other 4 episodes of Spartan Ops in online matchmaking?
No.
Currently, no. They are only using the first episode’s chapters at this moment in MM.
Unless 343 replaces the current episode (1) with another, then no. You won’t be able to play all four episodes in Matchmaking. In custom ops you can but you won’t get that much exp (though you can set the difficulty).