It is quite possible with a VBA macro. The table that you want to sort, you name it "newsorted". The cell as the first sort column named "column1", the cell under the second sort column is named "column2" and so on...All these names are examples used in the macro course! you put this macro in the sheet in question and whenever a cell changes value table is sorted.
It is obvious that this is a working example but it can be improved by ensuring that the modified cell is actually part of the table for example.
Private Sub Worksheet_Change (ByVal adrcel As Range)
Range ("Information"). Sort Key1: = Range ("column1") Order1: = xlAscending, _
Key2: = Range ("column2") ORDER2: = xlAscending, _
Key3: = Range ("column3") ORDER3: = xlAscending, _
Header: = xlYes, OrderCustom: = 1, MatchCase: = False, _
Orientation: = xlTopToBottom