Most recently, she was managing director of investor relations at Audax Private Equity in San Francisco.
The pair will advise Warburg Pincus on new investments and drive value creation across its portfolio companies.
Previously, Sharma was CEO and co-founder of InStride.
George Collier has also been appointed as chief operating officer.
Stephen Burhenn is appointed as a principal and Derrick Lee has joined as vice-president.
Tom Ehrhart and Mark Springer were promoted to managing directors.
Weber joins from Riverside, a mid-market private equity firm.
Critchlow joins from Next Wave Partners, a lower mid-market private equity firm.
Previously, Mehta was at Vector for 12 years.
Dollaga joins the firm following a career of more than 30 years in the US Navy.