Seronga has an airstrip (GPS: SERAIR) that is now in regular use from Maun bringing visitors to the Okavango Polers Trust, and this is now by far the easiest and most convenient way for most travellers to access this village. Check in Maun with Island Safari Lodge or Audi Camp for details of the options.
The only practical way to access the eastern side of the Panhandle with a vehicle is to cross the Okavango River on the ferry at Mohembo, in the far north.
There appears to be another route, which every year is tried by a clueless few, following what looks like a good road on the Shell map of Botswana. This appears to go around the eastern side of the Delta and link into Seronga from the Linyanti area, via the village of Betsha.
However, the tracks on this side have very few users and no signposts. They cross a number of different private concessions and hunting areas, none of which will welcome your visit. Straying off designated 'transit routes' will get you into trouble. Meanwhile, when the tracks meet villages they split and vanish. But perhaps the greatest danger here is of water levels blocking the route. It's easy to get dangerously lost in this region and to then run out of fuel, water or supplies. There's no help here, so I'd strongly advise against trying to use any of these tracks.
If you're travelling without a vehicle, then both Shakawe and Sepupa are fairly easy to access with one of the local busses that run up and down the road between Shakawe and Sehithwa. There are then two ways across to the eastern side.
The easiest way (and if you're aiming for Seronga, then the most convenient way) is to take the bus to Sepupa and then catch the small motor-boat ferry which shuttles between Sepupa and Seronga.
The alternative is to use the vehicle ferry at Mohembo, and then hitch south down the road on the eastern bank.
There's a regular motorboat ferry between Seronga Boat Station (GPS: SERBOA) and Sepupa. This takes a couple of hours to reach Sepupa (it's faster in the opposite direction, downstream), via a variety of winding channels. In the highly unlikely event that you ever need to navigate yourself to Seronga by boat, the turn-off from the main channel towards the boat station is at n SERTUR 18°49.776'S, 22°24.350'E, which is about 1.2km away.
On the motorboat ferry, a one-way trip costs only about P20 per person, but you'll have to wait for the boat to fill up. Alternatively, it may be possible to arrange boat transfers here from Guma Island Lodge on the west of the Panhandle, if you're staying there for a period of time. Sepupa Swamp Stop charges a minimum of P600 for a private motorboat to do the return journey between Sepupa and Seronga.