6 speed freewheel and 8 speed shifter/derailleur are never compatible. 7 and 8 speed are compatible with Campagnolo parts, but for the love of God don't do that.

7 speed Shimano pattern freewheel or cassette and 8 speed Shimano pattern shifting are not compatible, but can be coerced to kinda-sorta work poorly together. There's a 0.2mm difference in gear intervals that stacks up to 1.2mm discrepancy across the extremes. It's likely to make noise.