The members of the vortex monster class will all engulf you and cause an appropriate type of damage, except dust vortices, which will blind you, and fog clouds, which will do physical damage. Once you can survive their engulfing long enough to get yourself expelled with your horn or drum, their greatest danger is transporting you into lava or into a black dragon's disintegration blast.
Fog clouds offer a good opportunity for weapon training. While you are engulfed, your attacks are guaranteed to hit, avoiding the normal trouble non-warrior roles can have with the −4 Unskilled to-hit penalty. Despite messages like "You are laden with moisture and can barely breathe", they are not very dangerous because of their low speed. Pacifists might have problems with them if they can't move away since they mustn't destroy them.
As with fog clouds, dust vortices offer a good chance for beginning characters to train their weapon skills, particularly up to NetHack 3.6.0 since they dealt no physical damage. In NetHack 3.6.1, dust vortices are able to deal 1d6 physical damage if their attack fails to engulf you because you had been engulfed by them recently.
The energy vortex is a very dangerous monster to encounter for players who lack shock resistance, possessing both passive and active shock attacks. The passive attack is only triggered by melee attacks; ranged attacks, even when engulfed, are perfectly fine. This includes repeatedly throwing and picking up your melee weapon, if you have no more powerful alternative. It is sometimes necessary to use wands to survive an unfortunate energy vortex encounter. Normally, neither engulfing nor passive shock attacks will destroy your rings or wands; however, after the vortex releases you, its engulfing attack gets temporarily (for 1-2 turns) converted to a shocking touch attack, which can explode your items.
While engulfed, the energy vortex will drain your power 75% of the time, similar to an anti-magic field. If it drains your power below zero, it will reduce your maximum power. This can be particularly devastating if you can't kill it quickly; it can drain your max power all the way down to zero. Cancelling the vortex will prevent this, but magic cancellation will not, nor will magic resistance.
The energy drain attack was implemented in NetHack 3.6.0, where it was 4d6, making it even more dangerous.
Swirling clouds of pure elemental energies, the vortices are
thought to be related to the larger elementals. Though the
vortices do no damage when touched, they are noted for being
able to envelop unwary travellers. The hapless fool thus
swallowed by a vortex will soon perish from exposure to the
element the vortex is composed of.