Without Haste, what Efficiency level does a Pickaxe need to insta-mine Stone?

I found this website, which has a table about which tools can instant mine which blocks.

It seems an efficiency 5 diamond pickaxe will be able to instant-mine stone if you have haste 2.

It's hard to say which pickaxes other than diamond will be able to instant mine stone, but it seems your pickaxe's "speed" will need to be greater than 45 to instant mine stone.

Efficiency: additional (1+level2) when using the proper tool

This means an Efficiency 6 Diamond, Netherite or gold pickaxe should work. Efficiency 7 should be enough for any pickaxe to break stone.

So to answer your question: Both should be able to instant mine stone.

As for other blocks, that depends on which material the pickaxe is made out of. Take a look at the table on this page. The total speed needs to be at least 30 times the block hardness.

I'll answer

what other, harder blocks can they insta-mine?

Given pinckerman's answer, we have

Since you're asking for level 8 and 10 you get:

• Efficiency VIII gives 65
• Efficiency X gives 101

plus the value given by the material (8 for diamond, 9 for netherite).

Blocks can be insta-mined if the value above (e.g. 110 for an Efficiency X netherite pickaxe) is larger than 30 times the hardness value of the block:

If the tool and enchantments immediately equal or exceeds the hardness times 30, the block breaks with no delay

so (assuming a netherite pickaxe) with Eff X, you'll insta-mine blocks with hardness lower than 110/30 = 3.6666
with Eff VIII instead you'll insta-mine blocks with an hardness lower than 74/30 = 2.4666

Hardness values are listed here. Please do note that you also have to check if the block is optimally broken by a pickaxe, e.g. a wooden door with hardness 3 won't be insta-mined, as you need an axe, not a pickaxe.