Is is possible with Google Sheets to calculate the fields (currency) and ignore all fields that have had a strikethrough applied?
Cell formatting can not be used as a criteria on spreadsheet formulas as there's no formulas (AFAIK) that can grab a cell formatting.
It would be much easier if you'd have another column where you marked your values with a cell value change, like 'yes/no' or an 'x'.
You can do it in Apps Script. But relying in formatting to make calculations in Apps Script is tricky. I recommend have a menu triggered function that grabs the "strikethrough" format and generate a 'yes/no' column so you can use in regular formulas like SumIf.