Does anyone have insight into what these three schools emphasize in admissions. Hoping the answer will both shed light on how these schools differ and suggest strategies for targeting applications to each.
From what I’ve seen from Hamilton, they seem to value authentic applicants. To the extent that an attempt at targeting could interfere with the sincerity your approach, you might actually be best to avoid it. However, they do strongly value demonstrated interest.
The excellent Vassar tends to like highly qualified male applicants. So if you are male, make this clear in your application and during your interview. 
Most Important (MI)>Important (I)>Considered ©>Not Considered (NC)
Rigor- Hamilton (MI), Pomona (MI), Vassar (MI)
Class Rank- Hamilton (MI), Pomona (MI), Vassar (I)
GPA- Hamilton (MI), Pomona (MI), Vassar (I)
Test Scores- Hamilton (I), Pomona (MI), Vassar (I)
Essay- Hamilton (I), Pomona (MI), Vassar (I)
Recommendations- Hamilton (I), Pomona (MI), Vassar (I)
Interview- Hamilton (I), Pomona (I), Vassar ©
Extracurriculars- Hamilton (I), Pomona (MI), Vassar (I)
Talent/Ability- Hamilton ©, Pomona (MI), Vassar (I)
Personal Character- Hamilton (I), Pomona (MI), Vassar (I)
First Gen- Hamilton ©, Pomona ©, Vassar ©
Alumni Relation- Hamilton ©, Pomona ©, Vassar ©
Geographical Residency- Hamilton ©, Pomona (NC), Vassar ©
State Residency- Hamilton (NC), Pomona (NC), Vassar (NC)
Religious Affiliation- Hamilton (NC), Pomona (NC), Vassar (NC)
Volunteer Work- Hamilton ©, Pomona ©, Vassar ©
Work Experience- Hamilton ©, Pomona ©, Vassar ©
Applicant Interest- Hamilton ©, Pomona (NC), Vassar (NC)
SAT Mid 50% Range:
Hamilton: 1950-2220
Pomona: 2040-2300
Vassar: 1990-2240
ACT Mid 50% Range:
Hamilton: 31-33
Pomona: 30-34
Vassar: 30-33
% in Top 10% of Class:
Hamilton: 77%
Pomona: 92%
Vassar: 72%
% in Top 25% of Class:
Hamilton: 96%
Pomona: 100%
Vassar: 96%
Pomona is the most selective and weighs academics and personal qualities/extracurriculars more than the others do. Vassar and Hamilton have a more balanced approach, weighing each factor around the same. Only Hamilton indicates it considers applicant interest.
I think that Vassar is more of a ‘fit’ school than Hamilton or Pomona, meaning it suits you or it doesn’t; I think that Hamilton and Pomona suit a wider range of types of student. Definitely visit - if it suits you, you will know how to target your application.