Last I heard the roof was the "final Frontier" in terms of a problem yet to be solved, especially for those of us not living in an arid climate. I'd also be interested.. the closest I've come to finding an answer is work that Builders Without Borders has done in Mexico using remodeled pallets for trusses. (after which any sort of roofing material can be installed)
Trusses are not a bad idea. If you have the building skills available, you can do any conventional roof structure for your area. Pole barn, gable, hipped roof, shed, etc. Local 'norms' will usually handle snow or rain load. You may want wider eaves to protect your walls. (Some local 'norms' like postwar housing don't have any eaves to speak of. These roofs don't really protect the walls, but rely on 'modern' materials to protect the vulnerable wood inside. This doesn't work well for wooden houses, and would work even less well for your strawbale.)
I believe the normal thing for strawbale homes is to put a wooden 'bond beam' around the top of the bales, tied in with bolts or long staples. From this wooden ledge, you/your builder can build almost any roof as you normally would (e.g. from the top of a stud-framed wall, which has a similar wooden ledge on top).
If you are short on time, you can probably stack one wall higher than the others, lash some poles and a tarp across, and take some time to research it for the final version.
Should be some level of detail in most of the strawbale building books; message me if you don't have one and I will go borrow my father-in-law's copy to get you more info.
p.s. If you're looking for the 'right' answer, not just a workable one, options include:
Thatch: All-natural and biodegradable (but expensive, flammable, and hard to find in the USA)
Metal: Industrial material, but doubles as rainwater catchment and fire protection; much cheaper than thatch, and works in most locations. Cheap galvanized corrugated or fancier enameled sheet; some choice of colors.
Eco-Roof / Living Roof: Requires industrial material such as pond liner for waterproofing, but protects environment from stormwater and replaces some of green spaces lost to house footprint. Cob Cottage just puts pond liner over a curvy roof and then shovels on some upper-canopy material such as mosses (with live ferns, grass seeds, etc) from their own local forest. Other designs use drought-tolerant sedums and bunch-grasses; spring bulbs will also grow on/in living roofs. Price varies, as does durability and weight.
Boat / Tent: Any locally suitable material for boat-building can also make a weathertight roof. Bark, wood, waterproofed canvas over frame, etc. Cedar shakes are popular and long-lasting; other woods such as oak have also been used to make shakes or shingles. Can split your own or purchase split or sawn versions. Can be laid directly on purlins, or over tarpaper. On the plus side, roofs are easier to build than boats.
Ceramic tile: Spendy but pretty, looks good with the stucco-style exterior of finished strawbale, non-toxic, non-flammable, and durable.
Local conventional roof (asphalt tiles, roofing tar): easy to find, probably suitable for your climate, and relatively cheap to buy and install; may involve toxic materials or contaminate runoff.
Tarp, housewrap, or Tarpaper: Cheap and minimally effective way to decide not to decide this year. watch for leaks.
We put a couple pieces of rebar on top of the bales and laid down some of our mortar on top of the bales. Then we took some 2x10's with nails sticking out of them and laid them down with the nails into the mortar. Making sure they are level is greatly helpful, but not essential. Then fairly ordinary roofing technology can be laid on top of these 2x10 plates. The weight is distributed across the straw and the roof "floats" on top of the straw. What you do beyond that depends on your environment.