Algebro-geometric multigrid methods for solving large sparse systems of linear algebraic equations (SLAEs) arising from approximations of multidimension boundary value problems on embedded unstructured meshes are developed and investigated. The algorithms are based on the ordering of the nodes of the original mesh by their belonging to topological primitives of the coarse mesh: nodes, edges, faces and cells. With the corresponding numbering of vector components, the SLAE takes a block-three-diagonal form of the fourth order and is solved by preconditioned methods of incomplete factorisation with diagonal compensation in Krylov subspaces. Variants of sequential elimination of block-vector components as well as economical block bisection are considered. The results of numerical experiments with parallelisation of algorithms and their comparison with programmes from the Hypre library for a series of methodical examples with sevendiagonal SLAEs on cubic meshes are given. The prospects of development of the proposed approaches for solving wider classes of problems are discussed.