When does an overweight landing becomes necessary ?
The simple answer is when the risk of staying in the air is greater then the risk of an overweight landing .
When In non-normal situation is it a must to land as soon as possible even if the weight is above maximum for landing ?
An on-board fire.
I suppose there is a perception that if a plane lands overweight that the gear will collapse and the tyres will burst and the brakes will catch on fire. Overweight landings are not inherently a dangerous exercise, they just put a greater than normal stress on the aircraft (but will be within their design limits)
But I'm sure there are much more suitably qualified people than me who can give you some technical details/numbers