Yes, teachers and school administrators can conduct reasonable searches of students, their lockers, and even their cars.  Teachers and school administrators do not need a warrant or even probable cause to search a student.  All that is required is that the teacher or school administrator has a reasonable suspicion that a search will turn up evidence of a crime or violation of school rules.  If the teacher or school administrator finds evidence of a crime, that evidence can be turned over to the police. 

However, these are the rules that apply to teachers and school administrators.  Police officers that are on school grounds must still follow the standard rules of probable cause and the warrant requirement. 

Also, school officials are not allowed to strip search any student.  If a full strip search is necessary, the police would need to get involved and they would need probable cause. 

See S.C. Code Sections 59-63-1120 and 59-63-1140; N.J. v. T.L.O., 469 U.S. 328 (1985).