In dealing with similar cases in the past, where I could not just sort by a row, I found way to generate a column with a formula result that was something I could sort on.

I found a more direct answer to your question from this site: http://www.mrexcel.com/tip075.shtml

Microsoft Word has a feature which Excel is lacking. Jon's method involves moving the data to Word, employing the Word command and then pasting the data back to Excel. Follow these steps.
1. Copy the relevant chunk of rows and columns out of your speadsheet. It is best to note the size of the range, e.g., 118 rows x 5 columns
2. Paste the data into a Microsoft Word document, where it automatically becomes a table and retains all your formatting.
3. In Word, use the little-known SHIFT-ALT-UP-ARROW and SHIFT-ALT-DOWN-ARROW to very speedily slide rows (or selected chunks of rows) up and down at will. Select one or more rows. You can select the entire row or just a portion of the row as shown here.

Hit Shift+Alt+UpArrow several times in order to quickly slide the rows up into position. 
4. When you have sequenced the rows as you like, paste them back into Excel, making sure you overwrite the exact same size chunk you copied.
Thanks to Jon Von Gunten for this idea about making use of Word to solve this problem.

In dealing with similar cases in the past, where I could not just sort by a row, I found way to generate a column with a formula result that was something I could sort on.

I found a more direct answer to your question from this site:

Microsoft Word has a feature which Excel is lacking. Jon's method involves moving the data to Word, employing the Word command and then pasting the data back to Excel. Follow these steps.

1. Copy the relevant chunk of rows and columns out of your speadsheet. It is best to note the size of the range, e.g., 118 rows x 5 columns

2. Paste the data into a Microsoft Word document, where it automatically becomes a table and retains all your formatting.

3. In Word, use the little-known SHIFT-ALT-UP-ARROW and SHIFT-ALT-DOWN-ARROW to very speedily slide rows (or selected chunks of rows) up and down at will. Select one or more rows. You can select the entire row or just a portion of the row as shown here.

   

   Hit Shift+Alt+UpArrow several times in order to quickly slide the rows up into position.

   

4. When you have sequenced the rows as you like, paste them back into Excel, making sure you overwrite the exact same size chunk you copied.