What is long and what is short?

    Always short:    ε  and   ο.
  Either long or short  α and υ and ι can be either long or short. In most cases that is indicated by a macron over the vowel. Which makes for very complicated typing (and difficult reading, because in combination with other diacritics it becomes sort of fuzzy). It's generally pretty obvious anyway.
  Always long:     η  and ω  
and diphthongs: ει, αι, οι, ou...
  Odd man out  nominative/vocative plural endings -οι and -αι  count as short.
οἱ ἄνθρωποι    δοῦλοι        ἀγροί
αἱ ἄγκυραι       γλῶτται       ἑορταί
ἄγκυρα looks funny but pronounced "ankura" is not difficult to recognize as "anchor" (of a ship)
And γλῶττα appears in polyglot (who speaks with many tongues)