E/F/G: The Western Triangle
I always look forward to drawing one of these three countries because I see them as much more fun to play than other, more myopic countries (Turkey, mainly). Playing one of these three is also a good test of your skill as a diplomat or gunboater. All three are very strong countries, to be sure, but you don't have the luxury of a weak neighbor or a buffer of neutrals. It's a rare game of Diplomacy that Belgium, Holland, Sweden, and Norway aren't claimed by 1902. Negotiations between E/F/G are often tense, hinging on only a few territories and a few centers. For sake of this thread, I'll focus on gunboat only, but most of the same principles apply to full press as well.
There are a few key ideas to keep in mind in any game of Diplomacy, whether it's full press, public, or gunboat. Keep these in mind when strategizing (Jake Orion gives seven helpful tips at http://www.diplomacy-archive.com/resources/strategy/articles/opening_strategy1.htm). I paraphrase for gunboat:
Don't be overly aggressive.
Don't be greedy.
Don't push unless pushed.
DON'T BE OVERLY AGGRESSIVE
E/F/G exist in a quasi-balanced state at the beginning of the game. Each will have difficulty attacking the other without help from the third. In gunboat, you don't have the luxury of making definite plans with the other two, so all you have to go by are moves. This makes your opening moves all the more important. If you declare your intentions early on, it makes your moves that much more easy to counter.
DON'T BE GREEDY
In the E/F/G triangle, like I mentioned before, there are a limited number of centers from which to choose in 1901. England normally gets Norway, Germany normally gets Denmark and Holland, France normally gets Spain and Portugal, leaving Belgium as the only true "neutral" center. Belgium is usually the first point of contention between the three powers in F1901 and S1902. As such, it can usually determine how each power will approach the other two. This can be a luxury for England, as he can sit back and see how F/G approaches Belgium - does F build two armies, one fleet and one army, or two fleets? Does Germany build two armies or one of each? Is the fleet in Kiel or Berlin? Did France move his fleet to Portugal or Spain? Likewise, should England attempt to take Sweden early on, he sends a signal to France that his rear will likely be vulnerable. But by building two fleets to presumably attack England, Germany will be able to exploit your land weakness and easily push into Burgundy.
DON'T PUSH UNLESS PUSHED
This goes hand-in-hand with being greedy. Early aggression can often backfire. This goes for all countries in Diplomacy, but moreso for the E/F/G trio. Attacking only creates enemies, and sometimes more than one. E/F/G are nicely balanced and upsetting that balance can often have consequences for the aggressor.
To take this one step further, keep in mind the arrangement of centers and neutral spaces surrounding E/F/G home centers. Suppose that Germany gets bold and takes Burgundy in S1902, much to France's chagrin, as he has built two fleets. Germany can easily take Belgium, yes, but then what? France can still easily defend Paris and Marseilles from any incursion beyond Burgundy, the likelihood of which is slim when Germany only has five or six units as well as England to contend with. Likewise, should England get greedy and take the Channel in 1901, the likelihood of him advancing beyond Belgium or Picardy without Russia jamming him in the rear is low. The risk/reward for an early game attack is very low and will often result in a drawn-out stalemate which wastes both time and units.
So that, in an overly simplistic nutshell, is my take on the relationship between E/F/G in gunboat. Of course, Diplomacy is far more nuanced than I let on, and players are unpredictable, and there are no seven way draws. Keep those principles in mind, though, and you're likely prevent yourself from doing something stupid and maybe even doing well in a game or two.