I'm American, actually, although living in Germany. (It makes things interesting sometimes, because each country teaches classics a bit differently.) Almost everyone uses Smyth and the LSJ, though.
I don't know if there's an easy answer to your question. The phenomenon happening here is called "suppletion." Sometimes you'll see "defective verb" to describe verbs which don't have all principle parts.
I don't recall whether Smyth or Goodwin ever discuss this directly.
LSJ implies this information, but you have to know how to interpret it when they write:
"the place of the present εἴρω is supplied by φημί, λέγω or ἀγορεύω, and εἶπον serves as the aor."
Regarding weird verbs in general:
Smyth has a list of irregular verbs in the back of the book, I think, although it's cryptic as is usual for him. Can't give you a section number because my copy is across the Atlantic right now. There's probably something similar in Goodwin.
Kaegi's Greek Grammar (should be available via archive.org in English or German) also has an excellent table showing irregular verbs and their forms.
IPHIGENIE: Kann uns zum Vaterland die Fremde werden?
ARKAS: Und dir ist fremd das Vaterland geworden.
IPHIGENIE: Das ist's, warum mein blutend Herz nicht heilt.
(Goethe, Iphigenie auf Tauris)