to go through: to move all the way through or across something, from passing through a place to traveling about and, by extension, to news or death spreading and a blade running someone through
At its core this verb pictures motion that does not stop at the edge of something but carries all the way through it. The basic verb means simply to come or go; the prefix adds the idea of through. So the word can describe a single object pushed all the way through a gap (a camel through the eye of a needle), a person crossing a stretch of water, or someone walking through the middle of a hostile crowd.
From that physical picture the word naturally widens into the sense the book of Acts uses constantly: to travel about, going from town to town and region to region. This is the standard word for the missionary journeys, where the point is not arriving at one spot but moving steadily across a whole territory, often preaching along the way. A closely related shade keeps the focus on the destination instead, where the journey through is just the means of getting somewhere: let us cross over to the other side, go on as far as Antioch.
The same image of passing all the way through also carries two vivid figurative uses. A report can pass through a population the way a traveler passes through a country, so the word means to spread: word about Jesus spread abroad, and death spread to everyone. And a sword can pass through a body, so Simeon tells Mary that a sword will run through her own soul. In every case the underlying motion is the same: something moving completely through, not merely up to or past.
Because one Greek word covers this whole range, English has to keep changing words for it. There is no single matching verb, but the senses are clearly related shades of one idea rather than separate unrelated words.