I'm not entirely sure what you're asking. Do you mean what episodes are explicitly in continuity because they were referenced in the movies?
Oh, what the hell. I can't sleep so I may as well attempt to answer...
-TMP features Klingons, so presumably that brings all the Klingon episodes of TOS into the movie continuity. That would be "Errand of Mercy," "Friday's Child," "The Trouble with Tribbles," "A Private Little War," "Elaan of Troyius," "Day of the Dove," and "The Savage Curtain." An Andorian is also seen, so that brings in "Journey To Babel," "The Gamesters of Triskelion" and "Whom Gods Destroy" as well. (I'm not going to count Decker, since it's never explicitly said that he's the son of the guy from "The Doomsday Machine.") So that's 10 episodes.
-TWOK references "Space Seed," of course. Kirk & co. are teaching at Starfleet Academy, so according to this
script search, that adds in "Where No Man Has Gone Before," "What Are Little Girls Made Of?" "Court Martial," "Shore Leave," "The Changeling," "The Apple," "Bread and Circuses," "Obsession," "Patterns of Force," "Whom Gods Destroy," (again) and "The Way To Eden". McCoy brings Kirk Romulan Ale as a birthday present and the Neutral Zone is mentioned, so we can incorporate the Romulan episodes "Balance of Terror," "The Deadly Years," and "The Enterprise Incident." David Marcus mentions Surak, so that further confirms "The Savage Curtain." Since Saavik expresses surprise that Spock lied, I suppose that would also bring in any episodes that tell us that Vulcans don't lie. According to the
script search I just did, it looks like the earliest episode to do that was "The Menagerie." Spock's "Remember" to McCoy could perhaps be drawn from him telling Kirk to "Forget" at the end of "Requiem for Methuselah." That's 16 additional episodes, bringing the total to 26.
-TSFS again references "Journey To Babel" through the character of Sarek. Sarek mind melds with Kirk, so that brings in any TOS episodes featuring the mind meld ("Dagger of the Mind," "Return of the Archons," "A Taste of Armageddon," "Devil in the Dark," "The Changeling," "Mirror, Mirror," "By Any Other Name," "Spectre of the Gun," "The Paradise Syndrome," "Is There In Truth No Beauty?" "Requiem for Methuselah" again, and finally "Turnabout Intruder"). We see a Tribble in the bar that McCoy visits. We saw that Spock has the ability to place his consciousness or essence into a human being in "Return To Tomorrow." The regenerated Spock undergoes
Pon Farr, so that brings in "Amok Time." The
Enterprise self-destruct sequence is drawn from "Let That Be Your Last Battlefield" (almost word-for-word, IIRC). That's 14 more episodes, bringing the current total to 40.
-TVH uses the slingshot time-travel method introduced in "Tomorrow Is Yesterday" and reused in "Assignment: Earth." The movie again reuses Sarek and brings in Amanda for good measure. 2 more episodes = 42 total.
-TFF uses Klingons and Romulans again, and mentions Starfleet Academy. Sarek has a cameo in a flashback/dream sequence. I can't think of any references to TOS episodes not referenced before.
-TUC has Klingons, Romulans, Sarek, a mind meld, and Romulan Ale, but again, I can't really think of any brand-new TOS references.
Oh, wait. I just remembered that both Chapel and Rand appear in TMP and a few of the other movies. So that brings in their episodes. The new ones for Chapel would be "The Naked Time," "Operation -- Annihilate!" "A Private Little War," "The Immunity Syndrome," "And The Children Shall Lead," "Spock's Brain," "The Tholian Web," "For The World..." "Plato's Stepchildren," "Wink of an Eye," and "The Lights of Zetar." 11 more episodes = 53. For Rand, it's "Corbomite," "Enemy Within," "Man Trap," "Charlie X," "Miri," and "Conscience of the King." 6 new episodes = 59 episodes out of 79.
So there you go. According to the movies, 20 episodes of TOS never happened, but we still have Space Lincoln and space hippies, so it's all good.