それで details

Examples

and so — the result or consequence that followed

財布さいふを家いえに忘わすれちゃって。それで、走はしって取とりに戻もどったんだ。

saifu o ie ni wasurechatte. sorede, hashitte tori ni modotta n da.

I went and left my wallet at home. So I ran back to get it. casual

前まえの日ひから雨あめが続つづいていました。それで、グラウンドがぬかるんでいたんです。

mae no hi kara ame ga tsuzuite imashita. sorede, guraundo ga nukarunde ita n desu.

It had been raining since the day before. That's why the field was so muddy. neutral

引ひっ越こし先さきの近ちかくに大おおきな公園こうえんがあった。それで、犬いぬを飼かうことにした。

hikkoshisaki no chikaku ni ookina kouen ga atta. sorede, inu o kau koto ni shita.

There was a big park near the place we moved to. And so we decided to get a dog. neutral

so? and then? — asks the other person for the rest of the story

「昨日きのう、駅えきで先生せんせいに会あってさ。」「へえ、それで？」

"kinou, eki de sensei ni atte sa." "hee, sorede?"

"So yesterday I ran into the teacher at the station." "Huh, and then?" casual

ので
ので packs cause and result into one sentence and subordinates the cause, and it happily fronts a request (遅おくれますので、お待まちください); それで needs the cause already closed as its own sentence and only reports what followed — no request or command can follow it, where から／だから both allow one.
それから
Both carry a narrative forward, but それから only claims the next thing came next, while それで claims the previous sentence CAUSED it — swapping それで into a bare list of steps invents a causal link the speaker never made.
だから
それで reports the result that actually followed and will not carry an intention announced on the spot or a command after it (それで、もう寝ねるね and それで、早はやく帰かえりなさい both fail); だから asserts the speaker's own reasoning and fronts exactly those — dropping だから into a plain account of events makes it sound as if you are arguing a point rather than telling what happened.

じゃあ
One は apart from それでは — the formal end of the じゃあ entry — and both react to the last turn, but それで points backwards at a result that already followed (「それで？」asks for the rest of the story), while それでは／じゃあ points forwards and announces the next move.