The Effects of Large Static Magnetic Fields on the Human Nervous System
I don't know anything about long term health effects. The guidelines mentions that noticeable effects begin around 2 Tesla. This is in line with what I have heard. On the other hand, this mentions public exposure limits of 40 milliTesla. Here is a paper from the NIH that discusses health effects of neodynium magnets, but doesn't mention field strength.
Keep in mind that 2 Tesla is an extremely strong field. You are not likely to find it except right next to a large superconducting magnet. Or possibly between the poles of an exceptional research grade non-superconducting electromagnet.
Keep in mind that even if a strong magnetic field has no direct effect on a normal person, it could be harmful to a person with, say, a pacemaker.
Also, a field that strong can turn a stray piece of metal into a dangerous projectile.
Motion in a magnetic field matters because it exerts a force on moving electric charges. $\vec F = q \vec v \times \vec B$. This means for example, a copper wire feels no force, unless an electric current is moving inside it. In people, nerve impules are small brief currents. This may be why people feel effects in large fields. Walking means charges are moving faster.