A place where two roads meet and cross each others path
As you can see on the previous images an Unmarked Crossroads leaves very little for understanding who has priority and are possibly some of the most dangerous junctions, especially at night where someone may not even realise there is a crossroads ahead of them. In situations such as these, it has to be deemed that NO ONE has priority. Generally it will come down to what will allow for the ease of flow of traffic, maybe who got there first, are you crossing someone else's path, or whether it would be better to let others go first. There may be a line of sight issue where someone opposite can see easier than you and they may assist you to clear your junction first.
The safest advice that can always be given is if you don't know don't go until you consider it safe to do so.
As with most subjects, ALL road users need to work together to keep our roads safe, so be the defensive driver and assist each other no matter whether it's pedestrian, cyclist, Motorbike, car, van, bus, lorry etc. We all use the roads so let's help each other out and be considerate.
Crossing a vehicle's path at a crossroads carries a certain level of danger. However, of the two available methods (Blue path or Red path) the Blue path is considered the safest route to take.
This is crossing offside to offside with the oncoming vehicle
Vehicles that cross each other Offside to Offside will tend to have a better line of sight along the road throughout the turn.
Vehicles that cross each other Nearside to Nearside will tend to have a restricted view of what "might" be coming down the inside of the others vehicle.