Not the most elegant solution, but you could use a spreadsheet to calculate WKT (Well-Known Text) descriptions of your vertices, then import them as a geographic shape. For example, in Excel or OpenOffice, create a set of columns with the centre point coordinates (x and y) and the N/S/E/W distances you mention:
Point x y N S E W
Alpha 100 155 20 14 21.5 26

Then, make a column called WKT and use an equation to build the WKT string:
="POLYGON(("&B2&" "&(C2+D2)&", "&(B2+F2)&" "&C2&", "&B2&" "&(C2-E2)&", "&(B2-G2)&" "&C2&", "&B2&" "&(C2+D2)&"))"
Save as a tab-delimited text file, then use the "Delimited text" plugin to import the text file. The plugin should recognise the WKT field, and add the geometry as a layer.
