Sodha began her career as a research fellow in the director's research team at think tank the Institute for Public Policy Research in 2005. In 2008 she began working at think tank Demos as head of the capabilities programme.
In October 2010 she was hired by the Labour Party as senior policy adviser to leader Ed Miliband. At the Labour Party she also ran the Labour Party's Small Business Taskforce with entrepreneur Nigel Doughty.
- City Year UK, trustee
- Griffin Primary School, Wandsworth, vice chair and governor
- Guardian News and Media, freelance writer and occasional columnist
- First class MA (Oxon), Politics, Philosophy and Economics, University of Oxford, 1999-2002
- Master of Philosophy (MPhil), Political Science and Government, University of Oxford, 2003 – 2005