Their influence does not go beyond the nuclei of atoms. Electromagnetic force is a long range force like gravity. However, unlike gravity, it not only attracts but also repels depending on what charges are involved. Our universe seems to have an equal amount of positive and negative charges. Therefore, the attracting and repelling forces cancel each other out when they are spread out over a sufficiently large scale.
Gravity acts like an organizer that puts stars, galaxies, and clusters in order.