Let me think:
To increase students' awareness
The apostrophe is here to mark the possessive (to show that something has the following object, in this case "awareness") case of the noun it goes after, in this case "students". If you are talking about the awareness of a specific group of students, there should be a definite article before "students'". See the fourth case below if you'll keep as is.
To increase student awareness
This is a noun adjunct construction, used to mark the last noun in it as having something to do with the nouns right before it.
To increase students awareness
This is just grammatically incorrect. An accompanying noun adjunct does not take the plural form, unless a singular does not exist (e.g. clothes line, etc.).
To increase student's awareness
Slightly odd, but not wrong, per se. This sort of thing is usually used when referring to general concepts that are "possessed" by something. (e.g. prosecutor's immunity, fool's gold, ...)
"Student awareness" or "the students' awareness" are best here, in my opinion.