diff --git a/pandas/_typing.py b/pandas/_typing.py
index de02a549856ab..a99dc584f64ca 100644
--- a/pandas/_typing.py
+++ b/pandas/_typing.py
@@ -390,3 +390,13 @@ def closed(self) -> bool:
 ]
 AlignJoin = Literal["outer", "inner", "left", "right"]
 DtypeBackend = Literal["pyarrow", "numpy_nullable"]
+
+OpenFileErrors = Literal[
+    "strict",
+    "ignore",
+    "replace",
+    "surrogateescape",
+    "xmlcharrefreplace",
+    "backslashreplace",
+    "namereplace",
+]
diff --git a/pandas/core/generic.py b/pandas/core/generic.py
index 582a043a8a78a..8d7d66a1f1504 100644
--- a/pandas/core/generic.py
+++ b/pandas/core/generic.py
@@ -68,6 +68,7 @@
     Manager,
     NaPosition,
     NDFrameT,
+    OpenFileErrors,
     RandomState,
     Renamer,
     Scalar,
@@ -2566,7 +2567,7 @@ def to_hdf(
         nan_rep=None,
         dropna: bool_t | None = None,
         data_columns: Literal[True] | list[str] | None = None,
-        errors: str = "strict",
+        errors: OpenFileErrors = "strict",
         encoding: str = "UTF-8",
     ) -> None:
         """
@@ -2713,7 +2714,7 @@ def to_sql(
         index_label: IndexLabel = None,
         chunksize: int | None = None,
         dtype: DtypeArg | None = None,
-        method: str | None = None,
+        method: Literal["multi"] | Callable | None = None,
     ) -> int | None:
         """
         Write records stored in a DataFrame to a SQL database.
@@ -3559,7 +3560,7 @@ def to_csv(
         doublequote: bool_t = ...,
         escapechar: str | None = ...,
         decimal: str = ...,
-        errors: str = ...,
+        errors: OpenFileErrors = ...,
         storage_options: StorageOptions = ...,
     ) -> str:
         ...
@@ -3586,7 +3587,7 @@ def to_csv(
         doublequote: bool_t = ...,
         escapechar: str | None = ...,
         decimal: str = ...,
-        errors: str = ...,
+        errors: OpenFileErrors = ...,
         storage_options: StorageOptions = ...,
     ) -> None:
         ...
@@ -3617,7 +3618,7 @@ def to_csv(
         doublequote: bool_t = True,
         escapechar: str | None = None,
         decimal: str = ".",
-        errors: str = "strict",
+        errors: OpenFileErrors = "strict",
         storage_options: StorageOptions = None,
     ) -> str | None:
         r"""
@@ -4852,8 +4853,8 @@ def sort_values(
         axis: Axis = ...,
         ascending: bool_t | Sequence[bool_t] = ...,
         inplace: Literal[False] = ...,
-        kind: str = ...,
-        na_position: str = ...,
+        kind: SortKind = ...,
+        na_position: NaPosition = ...,
         ignore_index: bool_t = ...,
         key: ValueKeyFunc = ...,
     ) -> Self:
@@ -4866,8 +4867,8 @@ def sort_values(
         axis: Axis = ...,
         ascending: bool_t | Sequence[bool_t] = ...,
         inplace: Literal[True],
-        kind: str = ...,
-        na_position: str = ...,
+        kind: SortKind = ...,
+        na_position: NaPosition = ...,
         ignore_index: bool_t = ...,
         key: ValueKeyFunc = ...,
     ) -> None:
@@ -4880,8 +4881,8 @@ def sort_values(
         axis: Axis = ...,
         ascending: bool_t | Sequence[bool_t] = ...,
         inplace: bool_t = ...,
-        kind: str = ...,
-        na_position: str = ...,
+        kind: SortKind = ...,
+        na_position: NaPosition = ...,
         ignore_index: bool_t = ...,
         key: ValueKeyFunc = ...,
     ) -> Self | None:
@@ -4893,8 +4894,8 @@ def sort_values(
         axis: Axis = 0,
         ascending: bool_t | Sequence[bool_t] = True,
         inplace: bool_t = False,
-        kind: str = "quicksort",
-        na_position: str = "last",
+        kind: SortKind = "quicksort",
+        na_position: NaPosition = "last",
         ignore_index: bool_t = False,
         key: ValueKeyFunc = None,
     ) -> Self | None:
diff --git a/pandas/io/sql.py b/pandas/io/sql.py
index 0332cfb4adad7..d7f7a0b8801ed 100644
--- a/pandas/io/sql.py
+++ b/pandas/io/sql.py
@@ -23,6 +23,7 @@
 from typing import (
     TYPE_CHECKING,
     Any,
+    Callable,
     Iterator,
     Literal,
     Mapping,
@@ -683,7 +684,7 @@ def to_sql(
     index_label: IndexLabel = None,
     chunksize: int | None = None,
     dtype: DtypeArg | None = None,
-    method: str | None = None,
+    method: Literal["multi"] | Callable | None = None,
     engine: str = "auto",
     **engine_kwargs,
 ) -> int | None:
@@ -996,7 +997,9 @@ def insert_data(self) -> tuple[list[str], list[np.ndarray]]:
         return column_names, data_list
 
     def insert(
-        self, chunksize: int | None = None, method: str | None = None
+        self,
+        chunksize: int | None = None,
+        method: Literal["multi"] | Callable | None = None,
     ) -> int | None:
         # set insert method
         if method is None:
@@ -1402,7 +1405,7 @@ def to_sql(
         schema=None,
         chunksize: int | None = None,
         dtype: DtypeArg | None = None,
-        method=None,
+        method: Literal["multi"] | Callable | None = None,
         engine: str = "auto",
         **engine_kwargs,
     ) -> int | None:
@@ -1863,7 +1866,7 @@ def to_sql(
         schema: str | None = None,
         chunksize: int | None = None,
         dtype: DtypeArg | None = None,
-        method=None,
+        method: Literal["multi"] | Callable | None = None,
         engine: str = "auto",
         **engine_kwargs,
     ) -> int | None:
@@ -2318,7 +2321,7 @@ def to_sql(
         schema=None,
         chunksize: int | None = None,
         dtype: DtypeArg | None = None,
-        method=None,
+        method: Literal["multi"] | Callable | None = None,
         engine: str = "auto",
         **engine_kwargs,
     ) -> int | None: