I just can't figure out your question. Strawberries in the front row and then also in the back 2 rows? A trellis over the berries? What's your growing zone? Makes a difference on how much space to give tomatoes. They grow for longer in the south. I'm confused but here's what I'd do:
I'd put any trellis on the north side of your bed, hopefully it being the 6' side, for tomatoes. They won't shade your berries if they are on the north. I prefer stringing mine but I also use tomato cages for shorter determinates and stakes for tall vining indeterminate toms sometimes. If the toms need covering for any reason, too cold or against insects, wrap the covering around them in a circle and secure with binder clips or clothes pins.
I'd only use light weight row cover over the strawberries on the front side and remove it when blossoming so they can be pollinated by bees, insects, but cover them at nite against moths that lay eggs. This row cover also protects newly forming fruits from being eaten by birds. You need to read up a bit more on strawberry growing. There's several methods on this.
Whatever you do, have fun with it. Enjoy the experience and learn from any mistakes you make. The next year will be even more fun but harvesting that first tasty, ripe tomato is never forgotten. The flavor is unsurpassed as opposed to store-bought. Enjoy.

quiltbea spacing in square foot is by type of tomato not location of the grower.

dabsabre :please post a diagram of the plot in question because you description is confusing

sorry for the confusion.. I've got 2 rows of vine tomatoes and a row of strawberries in my 3x6 bed. The 2 rows of tomatoes are the north and middle row with the strawberries being the south row. I was looking for a way to incorporate a trellis for each of the tomato rows and a cage to protect the strawberries. I was mainly concerned with protecting the berries from birds while providing a trellis for each row of toms to grow the toms vertically.

Sorry you disagree greatcob but my friends in the south have much larger tomatoes than I do in the north so they benefit with 2' spacing in all directionS if they want good air circulation between the plants, especially with their heat. They grow around 10' tall but when temps loom over 90F they stop producing til it cools again.
dabsabre, you could put a trellis between the two rows or use stakes. Stakes have been used for decades with good results.
They sell bird netting which you can drop over your strawberries. Its open enuf for bees to pollinate yet protects from birds. I've used it before but it didn't protect against the grasshoppers that decided to invade my space.
Enjoy your new garden.