Washing one’s hands after scratching one’s head:
One who scratches [any area of the hair on] his head [with one’s hands] is required to wash his hands with water one time [immediately] afterwards. [This applies even if one only scratched his head with his pinky.] (However, one who merely placed his hands on his head, or even rubbed his head such as to dry his hair, but did not actually scratch between the hairs, is not required to wash. [Seemingly, this applies even by the normally covered areas of the head.])
Torah learning: It is forbidden to learn Torah or recite blessings after scratching the hair on one’s head, until the hands are cleaned. [Although it is necessary to wash one’s hands with water in order to remove the impurity that resides on the hands after scratching the head, as explained above, nevertheless,] to be allowed to learn Torah and recite blessings it is not necessary to specifically wash the hands with water. Rather, he may clean them with anything that cleans. This applies even if one has water readily available in front of him, nevertheless he may clean them in other ways.
Prayer: Prior to prayer [or in middle of prayer, prior to Shemoneh Esrei] one who scratches [the hair of] his head is required to wash his hands specifically with water.
Meal of bread: During a meal of bread, one who scratches (the hair of) his head is required to wash his hands again with water, following the same method as he washes for bread. Nonetheless, a blessing is not recited, [although one is to say a blessing without Shem Umalchus].
One who scratches his head, in between the hairs, is required to wash his hands immediately afterwards, and is not to learn Torah or pray or say a blessing until he cleans them.
If one scratched his head with his wrist, must he wash his hands?
If the fingers did not scratch the head, but rather only his palm or back of the hand, some write washing is not required.
Must one wash his hands if he scratched his head using a cloth?
Must one wash his hands after scratching a bald area of his head?
Must one wash his hand after scratching his beard?
 Admur Kama 4:18 [see also 92:7; 162:2; 164:2]; Michaber 4:18; Beis Yosef 4:18; Abudarham p. 369 in name of Tashbeitz; Kol Bo 23; See Mordechai Brachos Remez 194; Orchos Chaim Hilchos Netilas Yadayim 10; See Piskeiy Teshuvos 4:24
 Does this apply even if one scratches his head in the normally uncovered areas that stretch beyond his Kipa and hat? Some Poskim rule that this Halacha only applies to one who scratches his hair in the area that is normally covered by a Kipa, as only that area is considered to contain sweat. [Kaf Hachaim 4:98, based on wording of Michaber 4:21; Sheivet Halevy 8:2; Piskeiy Teshuvos 4:24] This, however, is not the simple implication from Admur who does not differentiate in this matter in Halacha 4:18 [or 92:7 or 164:2] and does not even bring the ruling of the Michaber 4:21 which discusses revealed areas. This follows the opinion of the Mamar Mordechai 4:11 who rules that if the head contains hair, then scratching even the normally uncovered areas require washing.
 One who is bald: See Q&A!
 Ketzos Hashulchan 2:11
 Admur ibid; M”A 4:17 in name of Mordechai; Taz 4:13; Elya Raba 4:12; Kisei Eliyahu 4:6; Yifei Laleiv 4:18 in name of Mor Uketzia; Peri Megadim 4 M”Z 14; Poskim in Kaf Hachaim 4:60
Other Opinions: Some Poskim rule that scratching the head does not bring an impure spirit and hence does not require washing with water. Rather the hand requires cleaning in any fashion in order to be allowed to learn Torah. [See Machatzis Hashekel 4:17; Nivei Shalom 4:12; Machazik Bracha brought in Shaareiy Teshuvah 4:12; Soles Belula 4:14 in name of Makor Chaim; Ben Ish Chaiy Toldos 17; Poskim in Kaf Hachaim ibid] Admur however rules that it causes impurity, and hence he rules only washing with water helps. So also rule other Poskim ibid
 Admur ibid; Kisei Eliyahu ibid; Yifei Laleiv 4:18 in name of Mor Uketzia; Peri Megadim 4 M”Z 14; and so is implied from many Poskim brought in Kaf Hachaim 4:60
The reason: This is due to that scratching the head causes impurity, and hence he rules only washing with water helps for all these actions. [Poskim ibid; Ketzos Hashulchan 2:11]
Other Opinions: Some Poskim rule that scratching the head does not bring an impure spirit. [See Machatzis Hashekel 4:17; Nivei Shalom 4:12; Machazik Bracha brought in Shaareiy Teshuvah 4:12; Soles Belula 4:14 in name of Makor Chaim; Ben Ish Chaiy Toldos 17; Poskim in Kaf Hachaim ibid]
 Ketzos Hashulchan 2:11; Kaf Hachaim 4:64 in name of Peri Megadim
 Admur 162:2 and 164:2 [regarding one who touches dirty areas during a meal, and the same would apply here as well regarding Ruach Ra’ah] Parentheses in original; Elya Raba 162:17; Chayeh Adam 40:19; Levushei Mordechai 1:12; M”B 162:58; Yifei Laleiv 23; Kaf Hachaim 4:74; Piskeiy Teshuvos ibid
Other Opinions: Some Poskim rule that one must wash his hands even if he merely touched the hair and did not scratch it. [M”A 162:14] Some conclude that if one contains a lot of sweat on his hair then he is to wash his hands afterwards. [Piskeiy Teshuvos 4 footnote 235 in name of Daas Torah]
 Setimas Haposkim ibid
 Admur 92:7; 164:2; Michaber 164:2; Rashba 1:912
 Admur Basra 4:1; 7:1; 92:6; Siddur Seder Netila; M”B 4:61; 227:11
Contradictions in Admur: In 613:4 Admur allows washing with water even on Yom Kippur, if one got his hands dirty in the process. This however does not mean to say that using water is an obligation, but rather simply that it is allowed. This also explains why he uses the word “permitted” and not “obligated” regarding this washing. However, TzAruch Iyun from Seder Birchas Hanehnin 13:17 where Admur rules that one who used the bathroom is required to wash his hands prior to saying the blessing over thunder and does not offer the ability to simply clean the hands on another item. The M”B 227:11 writes regarding that Halacha that one can either wash his hands or clean them in another method, and so writes Piskeiy Teshuvos 227:8. Vetzaruch Iyun.
No blessing: For this reason, according to all opinions, when washing prior to learning or reciting a blessing one does not say a blessing on the washing. [Basra ibid]
 Admur 92:6; Peri Megadim brought in M”B 4:61
 Admur Basra 4:1; 92:6-7
However even prior to prayer, if there is no water available, one may clean his hands with anything that cleans, as the verse does not specify a cleansing with using water. Nevertheless, before prayer it’s a mitzvah/obligation to walk up to a mil’s distance [18-24 minutes] to find water.
 See Admur 164:2 and Seder Netilas Yadayim 17
 Seder Netilas Yadayim 17
 See Piskeiy Teshuvos 4:23 in name of Chazon Ish
 Yifei Laleiv 1:27 brought in Kaf Hachaim 4:87; See Admur 97:3
 If the bald area is not normally covered by his Yarmulka, [such as one with a receding hairline], then the Poskim clearly rule that it does not require any washing at all, and does not prevent one from learning Torah. [Michaber 4:21; Mamar Mordechai 4:11; Kaf Hachaim 4:98; Sheivet Halevy 8:2; Piskeiy Teshuvos 4:24] Furthermore, even if the bald area is normally covered by his Yarmulka, and seemingly requires washing of his hands due to touching the normally covered areas, nonetheless, the Poskim imply that it never requires washing even in such a case. [See Admur 162:2 and 164:2 in parentheses; Elya Raba 162:17; Chayeh Adam 40:19; Levushei Mordechai 1:12; M”B 162:58; Yifei Laleiv 23; Kaf Hachaim 4:74; Piskeiy Teshuvos ibid]
The reason: As Admur rules that it is specifically the scratching between the hairs that causes the evil spirit to rest and prevents one from Torah learning due to the sweat, and hence if he has no hair then there is no reason to require the washing unless it is considered a normally covered part of the body.
 Kaf Hachaim 4:75; Ashel Avraham Butchach 4; Aruch Hashulchan 92:10; Sheivet Halevy 8:2 unlike Ruach Chaim 4:6