Strengthening Outcomes for America's Juvenile and Family Courts Act of 2010 - Amends the Victims of Child Abuse Act of 1990 to revise the grant program for juvenile and family court personnel to direct the Office of Juvenile Justice and Delinquency Prevention and the Office of Justice Programs in the Department of Justice (DOJ) to award grants to national nonprofit organizations with expertise in family law matters, including child abuse and neglect, elder abuse, and violence against women and family members, to improve training, education, technical assistance, and research to assist courts, judges, judicial personnel, attorneys, child welfare personnel, and lay child advocates in handling family law matters.