Of those listed, ALL are plenty strong enough ... I would place a priority on waterproofness instead. I would use any 'select' wood you can get ... plywood on edge if no voids or all voids on edge grain well sealed (below), same rules for LVL. For solid lumber, knot-free wood either with no defects or defects well-filled. Since you asked, LVL is designed to be a beam on edge, while plywood is not ... but for stiffening a deck, it's fine. Usually, solid lumber of square dimension is not rated as a beam either, but again, for stiffening a deck it's more than adequate.
Sealing end grain, edge grain, or wood defects: First coat edges with epoxy (repeat while wet) until the epoxy stays glossy for 10+ minutes. This indicates that no more saturation is occurring - the end grain will turn dull if the epoxy is still being absorbed. Cure. Sand corners to slightly round them and sand edge/end grain smooth. Vacuum off dust and wipe with damp towel and let dry. Mix cream slurry of epoxy and silica and coat edges with it to plug and fill all defects (microscopy on up to large and visible). I use a gloved hand to massage the silica mix into the wood and leave it smooth. Cure, lightly sand, add 2 seal-coats of clear epoxy.
Note that I, personally, follow the routine above for all edges. It's extra work, however, so I try to make sure I never have to do it ... bury edges in seams that have fillets of epoxy on them etc to avoid having to seal edge grain. It's unavoidable on ends of nailers and bottoms of deck supports that are made from some type of ply (seal bottom edge before installation) - which is why, for the aforementioned deck supports, I'd go with dimensional lumber and would just fillet where they meet the stringers. Just my 2-bits. For the record, I own a 20 year old skiff that has plywood sealed as above and was stored outside in weather for most of it's life, and the plywood edges sealed as above have never failed ... look good as new (see below).
Brian
