First, a side note: I play the black side of the French Defense almost religiously, and my results against the Exchange variation have traditionally been very good. It's not a variation that's feared by most French Defense practitioners. Neither, for that matter, is the Advance variation, which gives black a very clear plan of strategic counterattack based on undermining the white center, freeing the poor light-square bishop, and sometimes pressuring the white queen-side pawns. There are also lesser-known closed lines of the Advance involving a
...c4 pawn push that, while objectively tend to lead to equality, are very promising for the black player who is more familiar with their nuances than his opponent. If you really want to give French players trouble, consider learning to play (one of) the Tarrasch, Steinitz, or Classical variations.
Anyway, back to your main question. Normally, it's asymmetry of position that informs/determines the respective strategies that both sides attempt to realize. The exchange variation, however, is inherently symmetrical and therefore no clear, overarching strategies present themselves until the symmetry is broken by either white or black. There are a few proactive ways of creating asymmetry in this variation:
4. c4 which usually leads to IQP positions with all the attendant and characteristic advantages and disadvantages. The player with the IQP is advised to play aggressive, attacking chess and avoid liquidation of material (unless doing so yields an obvious benefit), as the IQP could be easily blockaded and made into a major weakness in the endgame.
- Preparing queen-side castling and launching a pawn storm if black chooses to castle king-side. This is highly double-edged and possibly questionable in its soundness, but a viable choice if you enjoy very sharp games and are confident in your tactical abilities.
Other moves are mostly noncommittal and give black time to develop as he chooses. Ultimately, if neither side breaks symmetry in any substantial way, the game is probably going to revolve largely around control/occupation of the squares e4 and e5. Further, numerous minor piece trades are very likely to take place on the e-file in such situations, leading to drawish positions.
One general piece of advice I'd offer, if you insist on playing the Exchange variation at all, is to delay it by one move and play
3. Nc3 first. In that case, if black opts for the Winawer variation with
3... Bb4, there's an argument to be made that, after
4. exd5 exd5 5. a3, black simply doesn't have any great choices (i.e., he must either effectively waste a move retreating the bishop, or cede the bishop pair, when the doubling of white's c-pawns could even be viewed as an asset in many situations because of their superior centralization). On the other hand, if black plays classically with
3... Nf6, he has lost the possibility of playing the pawn to f6 (often a good choice in many lines of the exchange variation because it helps to control the key e5 square and restrains white's minor pieces).