There are a few main benefits for having a podded engine,....
The engine and auxiliary equipment are podded, facilitating engine change - a lot easier to get at with no aircraft structure round it (most engines can be accesses by engineers on the ground, with no "cherry picker" or scaffolds needed (some turn arounds require a top up of oil, or something may need to be checked)..... this saves time and money. A podded engine also makes a complete engine change easier,.......
A podded engine will result in a lighter structure - burying the engines in the wing like the nimrod is aerodynamically more efficient as there is less flow distrubance, but the extra beefing up of the structure required is a downside. A podded engine will create much flow disturbance on the upper surface at high angles of attack, lowering the CLmax (increasing stall speed), and the nacelle strakes you se either side of some engines are there to create a vortex which promotes flow attachment until a higher alpha.
(Its been a while) The fact that the engines are podded makes the vibrational analysis (modes of vibration) a bit simpler to do - I was sat beside the Nimrod boys as they were carrying out this study and it was a nightmare,.... especially as the gear was also connected to the structure around the Nimrod engine.
In the event of an uncontained failure, there is less of a risk of the blade piercing vital control lines,..... even though redundancy is built in with this design case in mind.
Podded engines also allow for quieter cabins,..... obviously depends on where your sat and the aircraft concerned, but you get my drift,......
Another downside is due to the fact that the thrust line is well below the aerodynamic centre,.... means that when you add power, there is a large pitch up moment which needs to be counter acted with nose down (unless you fly the Airbus!),....
Hope this helps!
FP