The following records were searched without locating any Sterry or variant:

Quarter Sessions 1700-1799 [a name index to the Surrey Quarter Session Calendars for 1700-1799] [Source: LDS Film 6036505]
Quarter Sessions: NOTE BOOK OF A SURREY JUSTICE. By GRANVILLE LEVESON-GOWER, Esq., F.S.A. [Source: Internet Archive]
Surrey Assize 1565-1600 [Source: CD at Society of Genealogists, London]

Sterry records were found in the following records:
Surrey Quarter Sessions 1659-1668
Source: East Surrey Family History Society [fiche]

George Sterry appears as a surety in the Surrey Quarter Session records for 1661:
12 Aug 1661 Richard Jones of St Saviour victualler in 20 pounds: sureties George Sterrey shipwright and John Davis tailor (both) of the same in 10 pounds each. Condition: To appear ... to answer ... and not to depart ... and meantime to keep the peace ... especially towards Thomas Wilkinson.

This is George Sterry who died in 1685 at St Saviour's Southwark on the Ruardean Sterry line.

Nathaniel appears in three related Surrey Quarter Session records for 1662 as a witness:
[m. 95] John Willis late of St Thomas yeoman, being as [m 90] being over sixteen years of age on 6 July 1662, joined in an unlawful assembly there 10 Aug 1662 etc as [m 90] Endorsement: Herbert Dover, Nathaniel Sterrey sworn in Court

[m.68] John Willis late of St Thomas Southwark yeoman with others unknown to the number of twenty, 10 Aug 1662, forcibly ... there, under pretext of the exercise of religion, etc as [m61]. 11. Endorsement: Nathaniel Sterrey and Herbert Dower sworn in court. Insertion above line: Commiss' le gaol

[m 217] Also before John Lenthall kt., J.P., 10 Aug 1662 Herbert Dover of Lambeth victualler and Nathaniel Sterrey of St Saviour cooper in 20 pounds each [58]. Condition: To appear ... to prosecute and give evidence against John Willis for being at an "unlawful convention" and for refusing to take the Oath of Allegiance.

This is Nathaniel Sterry 1628-1698 on Ruardean Sterry line