"She trudges, schlepps, trains, drags, trascines her load": for one brief moment in Proteus, Stephen exercises his multilingualism in a single sentence, as if he is contemplating forging a polyglot portmanteau of the sort that Joyce strewed throughout Finnegans Wake. The verbs all mean roughly the same thing, and they appear to refer to the gypsy woman he is watching on the tide flats.
"Trudge" and "drag" are English, differing chiefly in that one is intransitive (walking heavily along, as in exhaustion) and the other transitive (pulling something heavy behind one). "Schlepp" is German for dragging something or for trudging. "Train" comes from French traîner, to drag something or to lag behind. "Trascine" is from Italian trascinare, to drag or (formed reflexively, trascinarsi) to drag oneself along, lag behind.
Gifford suggests that "The reference is to Eve, whose load of 'sorrow' was 'greatly multiplied by the Fall (Genesis 3:16)." But Genesis never calls Eve's suffering a load or burden, and for "She" to refer to Eve, one would have to assume some female personage in the previous sentence, which evokes the exile from Eden but never mentions either Eve or Adam.
The much more reasonable assumption is that "She" is the gypsy woman that Stephen has been contemplating for a good long while. She has "Spoils slung at her back," and both she and her partner have already been textually engaged in the first of these verb-actions: "Shouldering their bags they trudged, the red Egyptians." Just before Stephen searches for international synonyms for "trudge" (perhaps inspired by these international travelers), he has noticed one of them looking his way: "Passing now. / A side eye at my Hamlet hat."