How can I average individual cells that are >0 but NOT in a continuous range?

Something like this might do what you want. You can include additional ranges:

=AVERAGEIF(UNION.RANGES(0,B2:B3,C6:E8),">0")

Or rearrange/redesign your spreadsheet so the things you want to average together are together in a contiguous range or only blank cells or text between them (both of which are ignored by most numeric fucntions, such as averageif)

Can you show your work.

Most specifically, what do you mean by 'not in a continuous range'? That could be interpreted many ways.

For example, a column of values with gaps in the middle could be construed as 'not in a continuous range'.

But maybe you mean multiple, non-adjacent columns, which is a little harder to do. For this, you likely need to calculate the respective SUM() and COUNT() values and divide them.