Difficult to say in general since the optimal EOR strategy depends on the reservoir and the field being offshore is more a constraint on amount of wells and supply of chemicals. I suppose any method that requires low chemical volumes to be transported offshore, and methods that can utilize those chemicals effectively.
Miscible injection or (WAG) water-gas injection could be an optimum EOR strategy, depending of reservoir fluid and if yoh have sufficient gas to (re)inject in reservoir.
It depends very much on the local geology and fluid composition. For example: offshore Gulf of Suez, water drive (by injecting sea water) is generally used, with some complicacy due to scaling in the production pipes to shore after a while.
it is difficult to predict as it depend on the type of primary energy methods,lithology,and hydrocarbon"s properties .It might be overall cost effective methods of using sea(salty)water as injecting fluid for applying EOR techniques.but results may varies field to filed and PPM value of salts presence in water.
The mostly employed EOR method is Thermal EOR, but as mentioned above it depends on your reservoir and fluid type along with geology which method would be the best suited one. I have tried detailing the EOR methods in a mall paper. The link for paper is: http://oges.info/library/138473/
Offshore means issues with drilling locations, deck space, logistics, safety and more generally higher costs. Which EOR method is best is mostly function of reservoir and oil properties and previous developments if any. Henceforth being offshore has a bearing on "which EOR method is best" but that is mostly in relation with costs. This indirect impact explains why EOR methods, globally not that used in general, are even less used offshore. The more costly (e.g. thermal) being even less used than the least expensive (e.g. WAG). I can add a few things specific to offshore implementation of EOR for some methods (polymer, thermal, etc) but would rather see the initial query elaborated a bit.
You really have to specify what you are trying to do. EOR is a VERY wide subject, so what your asking is like "What is the best onshore car ?" There are so many possibilities, it is difficult to even start. So start by explaining what you're looking for.
The reservoir production drive is very important in order to determine the type of EOR. Generally speaking, waterflooding and WAG are the most commonly used methods. However, the type of formation damage they may create also changes selection strategy.