Not something to be underestimated, Meganium can play two distinctly different roles and potentially excel at both. Synthesis and dual screens, coupled with Meganium's solid defense stats and notable resistances—Electric, Water, and Ground—make it a wonderful supporter that can switch in on numerous threats. If that role is not needed, Meganium can also generate some offense with Swords Dance while still staying around with Synthesis. Should one opt for the Swords Dance set, be able to get Skarmory and Zapdos out the way.
Meganium is one of the best BL Pokémon with its great defenses and support movepool. Use whatever screen your team needs more, and if it can stay in and absorb an easy hit, Leech Seed the opponent to make switching in a teammate easier. Synthesis keeps Meganium alive for a long long time, and though Razor Leaf has a weak Base Power, it does have a high critical hit percentage (about 24% chance every time it is used), has a lot of PP unlike Giga Drain, and is super effective on Rock, Ground, and Water Pokémon, which helps keep Pokémon like Tyranitar, Marowak, and Starmie in check.
Should one feel like it, Meganium can also drop Leech Seed and sport both Reflect and Light Screen. This can go quite a long way to help a sweeper set up.
Meganium sadly lacks a physical STAB, but it has things going in its favor should one decide to use Swords Dance. Unlike most Swords Dance users, Meganium is naturally bulky, has an instant recovery move, and has good physical attacks in Body Slam—the paralysis bonus is amazing—and Earthquake. The beauty in Body Slam is its ability to cripple something like Starmie, who needs its speed to be effective. Try and keep this set hidden until the counters for it—Skarmory and Zapdos, mainly—are eliminated. From there, bulk up with Swords Dance and go to town.
One may be tempted to put a Grass STAB move here, but it's generally not needed. You're better off trying to paralyze Suicune and Starmie, and after a Swords Dance, either of the physical attacks will do as much or more than a super effective Razor Leaf. The only things that Razor Leaf or Giga Drain will do more damage to are Cloyster and Rhydon, which is far from enough to merit use over the 50% recovery of Synthesis. Rhydon will get hit hard with a +2 Earthquake anyway. Though Meganium doesn't pack the instant firepower of Exeggutor, it also isn't completely debilitated by Pursuit-carrying Dark types, which is something to consider.
Should you fear status afflictions, Meganium can also utilize Rest, but be aware that it is generally a bit difficult to pull off the two turns of sleep without Heal Bell support. Meganium also learns Counter, which is an awesome and underrated surprise move that will send Zapdos and Skarmory packing if they've taken any damage beforehand (remember that Counter also works on Hidden Power, so Hidden Power Ice Zapdos cannot circumvent the issue).
Checks and Counters
The support set is hard to take down, but Meganium won't be taking anything down itself, so most things sporting a super effective attack and/or a resistance to Razor Leaf can break through Meganium's defenses.
The Swords Dance set is walled by Skarmory and most Flying-types in general, including Charizard, Dragonite, Zapdos, and Aerodactyl. However, none of the aforementioned can afford to be paralyzed a lot, so fishing for paralysis with Body Slam is a good place to start. From there, something can set up to take them down and open the gates for Meganium.