You first need to decide whether or not Spirit Magic is used in your game. If not, see "Sorcerous Paladins". If you are using Spirit magic, see "Spiritual Paladins". For the spell ability of Paladins, see Magic.
These Paladins' Holy abilities would all be Spirit Magic or Divine Magic effects in RuneQuest. Give a Paladin the Spirit Magic spell of Heal, upgrade the level of Heal for every three full AD&D experience levels the character has. Thus, a 1st-2nd level paladin would know Heal 1, a 3rd-5th level Heal 2, and so on. A paladin also knows the spell Detect Enemy. Finally, the Paladin has a Countermagic 2 in constant effect upon him. These are all gifts from the paladin's deity. In return for this, the paladin must adhere to several Geasa, which consist of all the normal restrictions of paladinish behavior except that tithing is 90% instead of 10% (to keep paladins more in line with RuneQuest models of religion). Dereliction of any of the paladinic restrictions or requirements, no matter how slight, results in instant loss of all the above abilities.
Sorcerous Paladins don't fit as well, but they can be done. Instead of any innate ability, they have been assumed to have undergone an enchantment by the sorcerers of their church to be imbued with the spell Spell Resistance at intensity 2 and no INT cost. They carry a tattoo upon their person that holds the spell. They are also taught the spells Treat Wounds and Sense Enemy of the Faith. Finally, they are taught the Intensity skill to 3% times their AD&D level.
The only non-spell ranger abilities that needs conversion are their "animal empathy" and their "species enemy". Animal empathy would actually be a very high skill in the RuneQuest Animal Lore skill. Multiply a ranger's AD&D level by seven to determine their base rating in Animal Lore. The "species enemy" would best be simulated by the ability to cast a limited version of either the Bladesharp spirit magic spell or the Damage Boosting sorcerous spell. The limit is that the spell only works on a single species. Do not let your players choose which to use. Make the decision beforehand to be appropriate to your culture. If the "species enemy" is truly an innate ability and not learned nor teachable, then it should be spirit magic. If it is just another skill, then it should be sorcery.
The special abilities of Clerics and Druids are actually best handled as reusable Divine Magic in RuneQuest. "Turn Undead" is a specific spell found in Gods of Glorantha, a RuneQuest supplement.
In addition, RuneQuest deities also tend to value specific skills fairly highly. This is explained further in converting priestly magic, below.
Druids have more abilities:
Thieves have several annoying abilities:
Many bardic abilities are simply a poor attempt to numerically handle roleplaying. Ignore the "influence reactions" and "combat inspiration" abilities. The magical item idenfication skill is simply a special Lore skill and should be treated as such. Give the bard a percentile rating in "Magic Items Lore" for RuneQuest.