Drag multiple vertices of different line features in QGIS

Possible workaround, maybe good as just temporary solution for few data:

1. Enable snapping (Settings --> Snapping Options...). Set snap to vertex and set some tolerance.

2. Create a "dummy" line feature snapped on vertices you want move.

3. In snapping option check Enable topological editing

4. Activate node tool and select vertices of "dummy" line and move (hold Ctrl for selecting more vertices).

5. Done, you can delete the "dummy" feature or choose proper symbology if you give it special attribute or value.

Problem solved: Just found out, that the QAD-Plugin ( https://plugins.qgis.org/plugins/qad/ ) supports moving of vertices from different features:

In QGIS 3.10 you can just activate the edit mode of the layer or the layers. In my case snapping is not activated. Use the vertex tool. Also here you can choose between "All Layers" or "Current Layer", depending if the lines you want to edit are in one layer or in different layers.

With this tool active you can select the vertices by rectangle. The vertices will be marked with a blue circle around them.

Next you click one of the vetices and then click on the spot where you want to move this vertex. And the other(s) will follow.