According to Jack Landers at Rule .303, John Edwards managed to submit 10,081 signatures to get onto the Virginia primary ballot...while Richardson and Kucinich each slid in with 10,000 signatures even. However, since there is bound to be a variable amount of invalid/disqualified signatures, none of those 3 may actually make it onto the ballot if the signatures are challenged. If any candidate challenges the signatures, they are reviewed one-by-one.
As Jack also points out, it would be in Barack Obama's best interests to challenge the signatures, because if he knocks Edwards off of the ballot, the race boils down to a two-candidate race in Virginia, and Obama will take all of the support he can get (most Edwards supporters, in my estimation, would prefer Obama to Clinton).
Richardson and Kucinich are pretty far down on the ladder, support-wise. However, John Edwards is polling a solid 3rd in all reputable Dem polls and is still considered to be a potential "Hillary spoiler".