Because the problem appears with multiple lenses and multiple SD cards, the most likely cause is the camera body rather than the lens or card. Based on the community replies, this looks like a sensor or internal camera electronics fault. One reply specifically identified it as likely sensor damage, and another noted it tends to show up more in low light or burst shooting, which can make an intermittent body fault easier to notice.

The practical solution is to have Nikon service inspect and repair the camera. There is no reliable user fix, and opening or attempting repair yourself could worsen the damage or affect warranty/service options.

In short: if the lines are repeatable across lenses and cards, send the D3100 in for service.