If you have three or more vertices with an odd number of edges pointing towards it, it will not be traversable because, during one stage, you will realise that if you go any direction, you need to turn back to reach the other vertex which will cross the line twice, and therefore not traversable.
If you have exactly two vertices with an odd number of edges pointing towards it, then you will have to begin at one of the vertices and end at the other vertex. You cannot start at any of the vertices with an even number of edges pointing towards them in this case scenario. This will result in an Euler path.
If you have one or no vertices with an odd number of edges pointing towards it, then you can begin with any vertex and therefore end at any vertex no matter what. These graphs may comprise both Euler paths and Euler circuits.