Help me understand jewels.

I cant seem to understand how jewels work. I see their stats but don't under stand how the radius comes into it. do you get those stats per node in the radius? do all nodes get a buff simply for being in the radius, regardless of the jewel? or does the jewel just have its own effects and are irrelevant of the radius? if it says + 10% cold damage, does it simply become a tile for + 10 % cold damage? or does it add that effect to all tiles in the radius? does it simply boost tiles that already have that effect?

I cant seem to find a clear explanation online so I thought I would come here and ask. thanks in advance.

Radius on jewels only matters on jewels that say "WITH 'X' NUMBER OF 'Y kind of nodes' within radius, 'Z' happens" or "Passives within Radius that do 'x' instead do 'y' now". Jewels with a radius are all unique jewels. If you are looking at a blue/yellow jewel, then radius doesn't exist.

instead of creating another thread i decided to post here. does passives that have not been allocated with a point still works if it is within the radius of a jewel?

like for example overwhelming odds requires 40 str for the effects to proc. does the str nodes in the jewel radius needs to be allocated with a skill point or it can be left blank but as the radius still covers the node it still works?

edit: how about might in all forms? does the stats passive needs to be allocated a point as well?

They don't need to be allocated (were needed previously but it was changed in one of last patches), currently just being in radius is enough. Of course, that applies only to jewels that say "if you have %amount% of %stat% in radius". For jewels which convert stat X to stat Y in radius you'll obviously need to allocate those stat points.
e: if that wasn't clear enough: you don't need to allocate nodes only for threshold jewels (the ones which change an associated skill gem); for all other kinds of jewels, including MiAF, you'll need to allocate points to actually get their effect(s).

hmm then i guess for might in all forms needs the passives to be allocated.