Is there any easy way to have oblique map projections in ArcGis.
It means all the crazy stuff that happens here https://www.jasondavies.com/maps/transition/ when geographical poles are placed elsewhere.
Can I edit projections this way or can I import them from somewhere?
In ArcGIS Pro you can create custom projected coordinate systems using any of the supported projections. You can also modify any of the existing projected coordinate systems.
You can find more instruction and explanation in this lesson: https://learn.arcgis.com/en/projects/choose-the-right-projection/#
For oblique projections, there are several supported in ArcGIS, for example: