Yes, there is a quirk here. Verb "учить" + object in Accusative sometimes means "to learn" and sometimes mean "to teach". Actually they are homonyms. Which one is used should be understood from the context. Usually if the object is animate then it is "to teach" else it is "to learn". In case of "to teach" meaning an indirect object in Dative can be used to specify what is to teach.

Examples:

• учить урок = to learn lesson (Accusative, direct object)
• учить сына = to teach a son (Accusative, direct object)
• учить жизни = to teach how to live (Dative, indirect object)
• учить сына жизни = to teach a son how to live (сына - Accusative, жизни - Dative)

Other verbs of the same root are:

• учиться, обучаться (+ object in Dative) = to study smth. (учиться математике)
• изучать (+ object in Accusative) = to study smth. (изучать математику)
• обучать (+ object in Dative + object in Accusative) = to teach smth. to someone (обучать математике студентов)
• выучивать/заучивать (+ object in Accusative) = to learn smth. by heart (заучивать стихотворение)

The answers might have been conflicting because "учить" has all the meanings that you mentioned. I'll try to explain the usage based on intended English meaning: "to teach", "to learn" or "to study".

To teach -> учить

Meaning: To transfer knowledge and skills; to teach, instruct, give lessons; to educate, bring up
Perfective: научить, обучить
Related Russian words: обучать, преподавать, давать уроки

(a) учить + Accusative = to teach somebody (e.g. учить детей)
(b) учить + Dative = to teach something (e.g. учить русскому)
(c) учить + Infinitive = to teach [how] to do (e.g. учить читать)
(d) combination of (a)(b) or (a)(c) (e.g. учить детей русскому; учить детей читать)

• Я буду учить вас русскому языку. (Acc. + Dat.)= I'll be teaching you the Russian language.
• Меня учат лучшие преподаватели. (Acc.) = I'm being taught/educated by the best teachers.
• Чему учит эта пословица? (Dat.) = What's the moral of this proverb? (lit: What does this proverb teach?)
• Отец учил меня фотографировать.(Acc. + Inf.) = My father taught me how to photograph.
• Кто вас учил водить? (Acc. + Inf.) = Who taught you [how] to drive?
• С какого возраста нужно учить детей читать? (Acc. + Inf.) = Since what age should one teach childrent to read?
• Не учите меня жить! (Acc. + Inf.) = Don't teach me [how] to live!
• Бабушка учила меня, что... (Accusative) = My grandmother taught me that...
• Она сама учила своих детей. = She was educating her children by herself.

To learn/study -> учить

Meaning: To memorize or assimilate by repetition.
Perfective: выучить
Related Russian words: изучить, учиться, выучиться, научиться, штудировать (to study thoroughly), зубрить (to cram)

(a) учить + Accusative = to learn something (e.g. учить историю)　　

• Я учу русский язык. — I study Russian.
• Я хочу выучить русский язык за пять лет. — I want to master the Russian language in five years.
  
• Он не хочет учить математику. — He doesn't want to study math.
• Ты выучил таблицу умножения? — Have you memorized the multiplication table?
• Они учили наизусть стихи Пушкина. — They memorized Pushkin's poems by heart.
• учить наизусть — to learn by heart

To learn/study -> учиться

This is a reflexive form of "учить"
Meaning: To gain new knowledge, skills and experience.

(a) учиться + Dative - to learn, study

• Я учусь играть на гитаре. - I'm learning to play guitar.
• Я учусь русскому языку. — I'm learning/studying Russian. (less common but possible version)
• Дети учатся на ошибках. - Children learn from their mistakes.
• Он учится в МГУ. - He's studying at MSU (Moscow State University).

To learn/study -> изучать

Meaning 1: To learn or master something during the process of study.
Meaning 2: To study by the means of a scientific research
Meaning 3: To study carefully; to explore; to come to know inside out English translations: to study, master; to explore, make a careful study of smth.

(a) изучать + Dative - to learn, study, master something

• Я изучаю русский язык. - I'm learning the Russian language. (also: studying, mastering)
• Историк изучает древнюю рукопись. - A historian is studying an ancient manuscript.
• Пожалуйста, внимательно изучите все факты.　- Please, make a close study of all the facts.
• Я хочу изучить все возможности. — I want to explore all the possibilities.
• Мы стали изучать, в чём дело. - We started exploring what was going on.

To teach -> преподавать

Basically, it means "to give lessons, to instruct, lecture; to be a teacher"

(a) преподавать + Accusative - to teach, lecture
(b) преподавать (used on its own in the sense of "to be a teacher/lecturer")

• Я преподаю русский язык. (Accusative) - I'm a teacher of Russian. (lit: I teach Russian language.)
• Я преподаю в университете. (no supplement) - I lecture at a university.

In addition, check out this forum discussion about To teach/to learn/to study.

There are few popular mistakes with this words:

If you have finished studying in University (for example) you can say it in this way:

• Я учился в университете.
• Я закончил университет. It's the best.

Not Я выучил университет and not Я выучился в университете

But if you have finished studying a poem or language you have to say

• Я выучил стихотворение or Я выучил русский язык

If you say Я учил русский язык it means that you used to study it but haven't finished.

And there is one very popular phrase "Жизнь научит" and "Жизнь покажет", they mean that some time later this man will understand something by himself because we have different things in our life: problems and goals, so we study all our life. This phrase isn't about God or something supernatural.

How to use:

1: You know, my neighbour borrowed money from me again. And he said that he won't return it! (Представь, мой сосед снова занял у меня деньги. Он сказал, что не отдаст их!)

2: I think that one time he'll have same situation and he'll understand that his behaviour is wrong. (Я думаю, жизнь его научит)