straight cut and helical refer to the teeth that always mesh together with the lay shaft (not reverse).
A layshaft looks like a christmas tree of gears all connected to or a part of a single shaft.
Syncros and dogs refer to the way that the gears (1-5 or 6) are selected and then connected to the shaft so that the power is transferred.
All the forward gears are on a shaft and when in neutral, spin on bearings. The shift lever connects to a fork that pushes a sliding ring that is geared to a hub that is permanently geared to the same shaft.
When you push the lever, the ring engages teeth (not the same ones that engage the layshaft, but other teeth on the side 90 degrees different)on the spinning gear and they connect the gear to the ring to the hub to the shaft and the car will move.
When you engage the spinning gear it needs to start spinning at the same rate as the hub or it makes noise. Synromesh is the way that a brake (syncro) starts engaging the hub and in turn, starts spinning the gear at the same speed so that the gears will mesh without noise. (a worn syncro (brake) can be beaten and gear noise results).
Dogs are a real coarse type of tooth (like 6 or 8 on a gear) with voids between them so that the teeth will drop in easily. There is no brake so double cluthing helps.
Once the gears are spinning, the dog teeth drop in easier. Close gears are also a help as the spinning speed differences are less.
a "dog" looks like this -
]- in a circle.
There are different type of syncromesh designs but they all are a form of brake.
Hope this helps.