What is the justification used by the Nazarene denomination that permits women to be pastors/ elders? Nazarenes allow for, and indeed pride ourselves on, our allowance of women in the pastorate. What is their justification for doing so?
The Church of the Nazarene publishes a Manual which details their theology and doctrine. In Page 186, paragraph 501, the justification for ordaining women is presented:


  501. Theology of Women in Ministry. The Church of the
  Nazarene supports the right of women to use their God-given
  spiritual gifts within the church and affirms the historic right
  of women to be elected and appointed to places of leadership
  within the Church of the Nazarene, including the offices of
  both elder and deacon.
  
  The purpose of Christ’s redemptive work is to set God’s creation
  free from the curse of the Fall. Those who are “in Christ”
  are new creations (2 Corinthians 5:17). In this redemptive
  community, no human being is to be regarded as inferior on
  the basis of social status, race, or gender (Galatians 3:26-28).
  
  Acknowledging the apparent paradox created by Paul’s instruction
  to Timothy (1 Timothy 2:11-12) and to the church
  in Corinth (1 Corinthians 14:33-34), we believe interpreting
  these passages as limiting the role of women in ministry presents serious conflicts with specific passages of scripture
  that commend female participation in spiritual leadership
  roles (Joel 2:28-29; Acts 2:17-18; 21:8-9; Romans 16:1, 3, 7;
  Philippians 4:2-3), and violates the spirit and practice of the
  Wesleyan-holiness tradition. Finally, it is incompatible with
  the character of God presented throughout Scripture, especially
  as revealed in the person of Jesus Christ.


As far as I can understand the text, the Church of the Nazarene states that ordination cannot be restricted to men only because "no human being is to be regarded as inferior on the basis of social status, race or gender" citing II Cor 5:17 and Gal 3:26–28 as support.

Furthermore, while recognising the direct instructions by St Paul (I Tim 2:11–12, I Cor 14:34–35) regarding the role of women in Church, they reject their literal interpretation by asserting they are in contradiction to passages that "commend female participation in spiritual leadership roles," citing Joel 2:28–29, Acts 2:17–18, Acts 21:8–9, Rom 16:1–7 and Phil 4:2–3, as well as furthermore being "incompatible with the character of God presented throughout Scripture, especially as revealed in the person of Jesus Christ."