とかで details

Examples

apparently; something about — gives the reason for what follows while marking it as hearsay the speaker has not checked

田中たなかさんは風邪かぜをひいたとかで、今日きょうは休やすみだそうだ。

tanaka-san wa kaze o hiita to ka de, kyou wa yasumi da sou da.

Something about catching a cold — apparently Tanaka is off today. neutral

急きゅうな用事ようじができたとかで、彼かれ、先さきに帰かえっちゃったよ。

kyuu na youji ga dekita to ka de, kare, saki ni kaetchatta yo.

Something came up, apparently, so he took off early. casual

担当たんとう者しゃが出張しゅっちょう中ちゅうとかで、ご返事へんじは来週らいしゅうになるとのことでございます。

tantousha ga shutchouchuu to ka de, go henji wa raishuu ni naru to no koto de gozaimasu.

The person in charge is away on business, it seems, so a reply will come next week. formal

Not the listing とか (パンとか卵たまごとか): here か marks the whole clause
as approximate, so the reason is quoted without the speaker vouching for it.

そうだ
そうだ relays the report as heard and stands behind the wording, and it ends the sentence; とかで hedges the content itself ("something about a cold") and is a mid-sentence connective supplying the REASON for what follows — 風邪かぜをひいたそうだ closes a sentence, 風邪かぜをひいたとかで欠席けっせきした cannot be split at the same point.
らしい
らしい presents outside information the speaker is willing to be held to; とかで signals the speaker never bothered to pin it down — quoting a figure as 三千円さんぜんえんとかで reads as carelessness about the number, where 三千円さんぜんえんらしい reads as attribution of it.
によると
によると names the source and stands behind what it relays (天気てんき予報よほうによると); とかで names neither the source nor the exact content, so it can carry a reason the speaker heard in passing and would not repeat under scrutiny.
から
Both hand the following clause its reason, but から asserts the reason as the speaker's own (雨あめが降ふったから中止ちゅうしした); とかで disowns it — the speaker reports someone else's stated reason without endorsing it, so it never explains the speaker's OWN action motive.