The inconsistency of Charles's reported birth date and place can be explained by the fact that he was orphaned as a teenager, and such children often lose track of their correct date and place of birth.  The date from the 1900 census is the one most likely to be correct because Charles was still living with his parents at the time.  (Note that Putnam and Hancock Cos. are adjacent.) 

1.  Marriage Record:

2.  1910 Census Index/Images (online at Ancestry.com, Image #14 of 17):  770 North Front St., Columbus City (Ward 10), Franklin Co., OH, Roll T624_1182, p. 164B, SN 7B, SD 11, ED 151, enumerated 27 Apr 1910, official enumeration date 15 Apr 1910 (extracted by Diana Gale Matthiesen):

1910:  for an explanation of the column headings, please see What the Numbers in the Federal Census Mean (missing columns contained no data).

1

2

3

4

5

6

7

8

9

10

11

12

13

14

17

18

19

20

21

22

23

24

25

26

27

28

143

143

Miner William D

Head

M

W

52

M1

28

OH

Unk

Unk

Eng

???

???

W

N

0

Y

Y

O

F

H

_____ Cathrine S

Wife

F

W

55

M1

28

1

1

OH

Ger

OH

Eng

None

Y

Y

_____ Margaret

dau

F

W

19

S

0

OH

OH

OH

Eng

None

Y

Y

Y

Radebaugh Chas

Boarder

M

W

21

S

OH

OH

OH

Eng

Clerk

C & E Shoe

W

N

0

Y

Y

This Charles RADEBAUGH may not be our subject, but he's the only likely one I could find.  Both of his parents are deceased in 1910.

2.  1920 Census Index/Images (online at Ancestry.com, Image #23 of 28):  509 Ryan St., City of Fort Worth (Ward 9), Tarrant Co., TX, Roll T625_1850, p. 176A, SN 12A, SD 12, ED 138, enumerated 12 Jan 1920, official enumeration date 1 Jan 1920 (extracted by Diana Gale Matthiesen):

1920:  for an explanation of the column headings, please see What the Numbers in the Federal Census Mean (missing columns contained no data).

1

2

3

4

5

6

7

8

9

10

11

12

16

17

18

19

21

23

25

26

27

28

*

509

201

280

Rodebaugh Chas P

Head

O

F

M

W

33

M

Y

Y

OH

OH

OH

Y

Switchman

Steam Rail Way

W

_________ Julia

Wife

F

W

35

M

Y

Y

TX

IL

IL

Y

Hous Work

In House

_________ Chas Jr

Son

M

W

12

S

Y

Y

Y

TX

OH

TX

Y

None

*Ryan

Charles Jr. is Julia's son from her first marriage.

3.  1930 Census Index/Images (online at Ancestry.com, Image #11 of 38 — indexed "Charles G. Radebaugh"):  509 Ryan St., Fort Worth City (Ward 9C), Tarrant Co., TX, Roll 2394, p. 95A, SN 6A, ED 220-37, SD 9, enumerated 11 Apr 1930, official enumeration date 1 Apr 1930 (extracted by Diana Gale Matthiesen):

1930:  for an explanation of the column headings, please see What the Numbers in the Federal Census Mean (missing columns contained no data).
1	2	3	4	5	6	7	8	11	12	13	14	15	16	17	18	19	20	24	25	26	27	28	30
*	509	43	53	Rodebaugh Charles P	Head	O	1800	M	W	40	M	27	N	Y	OH	PA	OH	Y	Plumber	Building	W	Y	N
				_________ Julia	Wife			F	W	45	M	18	N	Y	TX	IL	IL	Y	None
*Ryan St

Listed next to Julia's son from her first marriage, Charles E. CHEESMAN (22, TX).