I want a report where there is an arrow on each column such that on clicking the arrow the sorting of the column can be changed.This means on clicking on the column for the first time if it is sorted in ascending order the next click should sort the same in descending order and so on. Can somebody please help me with this... I am working on version 7.1.4 and i want the output in HTML. Also without using OLAP.

Put a drill down on your title that passes the sort order and column name as two of its arguments.

Act it is required that the arrow points down while sorting is done in the ascending order and the arrow should point up while in the descending order. Can that also be achieved?

Yes, adding the image also possible.

Check for the direction(ascending or descending) in your define statement and change the image based on that.

Not exactly what you asked for but something you might consider is using the drillmenuitem stylesheet feature with options of "sort ascending by xxx" and "sort descending by xxx". You could also add "hide column xxx".
When using drillmenuitem features I always like to provide an alternate way (via a menu option) for the user to change the sorting just in case the user's browser does not render the drillmenuitems properly (I've had trouble getting firefox and drillmenuitems to play nice)
Also, regardless of browser considerations, if you do offer a "hide" feature then you should provide a way to "unhide" via a menu option.

Just a thought. This technique has served me well.