Google Sheets – Sort Column While Keeping Associated Values

I've added the result of your question in the Google Spreadsheet you shared with us.
In the SUMMARY sheet I collected all data that fits the criterion D<>0, with the following formula:

=QUERY(DATA!A:D;"SELECT A,C,D WHERE D<>0")

I also added an ID number, for the two companies and added the column to the summary sheet. As you can see, this formula can be easily extended.

You can achieve this by using an array of importrange() functions. This cannot import the formatting information, which is not possible without Apps Script, but it will pull in multiple sheets and aggregate them into one list, which you can then sort with an additional formula. Keep in mind that each imported sheet will have to have the same number of columns. For example, if you have four sheets to import with 4 columns each, the import formula will be as follows:

={
importrange("url_to_sheet_1", "Approved!$A:$D");
importrange("url_to_sheet_2", "Approved!$A:$D");
importrange("url_to_sheet_3", "Approved!$A:$D");
importrange("url_to_sheet_4", "Approved!$A:$D")
}