By adding or removing appropriate structures to Gauss diagrams, one can create useful objects related to virtual links. In this paper few objects of this kind are studied: twisted virtual links generalizing virtual links; signed chord diagrams staying halfway between twisted virtual links and Kauffman bracket / Khovanov homology; alternatable virtual links intermediate between virtual and classical links. The most profound role here belongs to a structure that we dare to call orientation of chord diagrams. Khovanov homology is generalized to oriented signed chord diagrams and links in an oriented thickened surface such that the link projection realizes the first Stiefel-Whitney class of the surface.