Emergency Social Security Benefits Improvement Act This bill makes changes to Old-Age, Survivors, and Disability Insurance (OASDI) benefits, including by (1) modifying funding formulas, (2) extending eligibility for certain benefits, and (3) increasing income thresholds used to determine the percentage of OASDI benefits subject to federal income tax. Changes to funding formulas include (1) increasing the primary insurance amount, and (2) establishing new methods to calculate benefits for individuals with lifetime low earnings and for widows and widowers. In addition, children of a deceased, disabled, or retired worker remain eligible for benefits through age 22 if they are full-time students. Under current law, they receive benefits through age 18. The bill also extends dependent child benefits to specified family members other than grandparents or step-grandparents, including in cases where a court grants custody of the dependent child to an eligible family member. To receive benefits under current law, either both parents must be disabled or deceased or a grandparent or step-grandparent must legally adopt the dependent child.