Have you tried using the SQL "IN" Operator?
SQL IN Operator
http://www.w3schools.com/sql/sql_in.asp
lyr = r"<NAME_OF_LAYER>"
oid = [12, 13, 14, 15]
sql = "{} IN ({})".format("OBJECTID", ", ".join([str(n) for n in oid]))
arcpy.management.SelectLayerByAttribute(lyr, "NEW_SELECTION", sql)
The above format and list comprehension would yield the following string:
'OBJECTID IN (12, 13, 14, 15)'
The trick to this is that you need to create a string that represents valid SQL Syntax. This can be done is quite a few ways. I've listed a few quick options below.
sql = " OR ".join(["OBJECTID = {}".format(n) for n in oid])
sql = "{0} >= {1} AND {0} <= {2}".format("OBJECTID", min(oid), max(oid))
sql = "{} BETWEEN {} AND {}".format("OBJECTID", min(oid), max(oid))