The 32-year-old Strevens was released by Wycombe following their relegation from League One and has signed a one-year deal.
Strevens, who counts Brentford and Barnet among his former clubs, impressed in a behind-closed-doors friendly against Dagenham in midweek.
Gills boss Martin Allen returned to former club Notts County to secure midfielder Allen and goalkeeper Nelson, who were both released in May.
Allen, 20, has penned a one-year contract, with the option of a further year, while Nelson, 30, has put pen to paper on a two-year deal.
