10 deleted 197 characters in body
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 List1 = {{23, 24, 251, 262}, {23, 24, 25, 261, 272, 283}, {23, 24, 251, 262, 273, 284, 295}};
 List2 = {{231, 242, 264, 308, 297}, {23, 24, 26, 291, 302, 319, 3210}};
 List3 = {{319, 3311, 231}, {231, 319, 3311, 3513}, {23, 31, 331, 349, 3512}, {23, 31, 331, 349, 3514}};
FinalList = {{23, 24, 25, 26}, {23, 24, 25, 26, 27, 28}, {23, 24, 25, 26, 27, 28, 
29}, {23, 24, 25, 26, 27, 28, 29, 30}, {23, 24, 25, 26, 27, 28, 29, 
30, 31, 32}, {23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33}, {23, 24, 
25, 26, 27, 28, 29, 30, 31, 32, 33, 35}, {23, 24, 25, 26, 27, 28, 
29, 30, 31, 32, 33, 34, 35},{23, 24, 25, 26, 27, 28, 
29, 30, 31, 32, 33, 34, 35}}
{{1, 2}, {1, 2, 3}, {1, 2, 3, 4, 5}, {1, 2, 3, 4, 5, 7, 8}, {1, 2, 3, 
 4, 5, 7, 8, 9, 10}, {1, 2, 3, 4, 5, 7, 8, 9, 10, 11}, {1, 2, 3, 4, 
 5, 7, 8, 9, 10, 11, 13}, {1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 12, 
 13}, {1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 12, 13}}
List1 = {{23, 24, 25, 26}, {23, 24, 25, 26, 27, 28}, {23, 24, 25, 26, 27, 28, 29}}
List2 = {{23, 24, 26, 30, 29}, {23, 24, 26, 29, 30, 31, 32}}
List3 = {{31, 33, 23}, {23, 31, 33, 35}, {23, 31, 33, 34, 35}, {23, 31, 33, 34, 35}}
FinalList = {{23, 24, 25, 26}, {23, 24, 25, 26, 27, 28}, {23, 24, 25, 26, 27, 28, 
29}, {23, 24, 25, 26, 27, 28, 29, 30}, {23, 24, 25, 26, 27, 28, 29, 
30, 31, 32}, {23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33}, {23, 24, 
25, 26, 27, 28, 29, 30, 31, 32, 33, 35}, {23, 24, 25, 26, 27, 28, 
29, 30, 31, 32, 33, 34, 35},{23, 24, 25, 26, 27, 28, 
29, 30, 31, 32, 33, 34, 35}}
 List1 = {{1, 2}, {1, 2, 3}, {1, 2, 3, 4, 5}};
 List2 = {{1, 2, 4, 8, 7}, {1, 2, 9, 10}};
 List3 = {{9, 11, 1}, {1, 9, 11, 13}, {1, 9, 12}, {1, 9, 14}};
{{1, 2}, {1, 2, 3}, {1, 2, 3, 4, 5}, {1, 2, 3, 4, 5, 7, 8}, {1, 2, 3, 
 4, 5, 7, 8, 9, 10}, {1, 2, 3, 4, 5, 7, 8, 9, 10, 11}, {1, 2, 3, 4, 
 5, 7, 8, 9, 10, 11, 13}, {1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 12, 
 13}, {1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 12, 13}}
9 deleted 11 characters in body
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`

Producing

`

FinalList = {{23, 24, 25, 26}, {23, 24, 25, 26, 27, 28}, {23, 24, 25, 26, 27, 28, 
29}, {23, 24, 25, 26, 27, 28, 29, 30}, {23, 24, 25, 26, 27, 28, 29, 
30, 31, 32}, {23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33}, {23, 24, 
25, 26, 27, 28, 29, 30, 31, 32, 33, 35}, {23, 24, 25, 26, 27, 28, 
29, 30, 31, 32, 33, 34, 35},{23, 24, 25, 26, 27, 28, 
29, 30, 31, 32, 33, 34, 35}}
FinalList = {{23, 24, 25, 26}, {23, 24, 25, 26, 27, 28}, {23, 24, 25, 26, 27, 28, 
29}, {23, 24, 25, 26, 27, 28, 29, 30}, {23, 24, 25, 26, 27, 28, 29, 
30, 31, 32}, {23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33}, {23, 24, 
25, 26, 27, 28, 29, 30, 31, 32, 33, 35}, {23, 24, 25, 26, 27, 28, 
29, 30, 31, 32, 33, 34, 35},{23, 24, 25, 26, 27, 28, 
29, 30, 31, 32, 33, 34, 35}}

Edit

EDIT: With @ciao's help, I have the solution

Edit 2

EDIT 2: Fidgeting around for a bit, I realized on dropping the outer Union, the problem is solved.

`

Producing

`

FinalList = {{23, 24, 25, 26}, {23, 24, 25, 26, 27, 28}, {23, 24, 25, 26, 27, 28, 
29}, {23, 24, 25, 26, 27, 28, 29, 30}, {23, 24, 25, 26, 27, 28, 29, 
30, 31, 32}, {23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33}, {23, 24, 
25, 26, 27, 28, 29, 30, 31, 32, 33, 35}, {23, 24, 25, 26, 27, 28, 
29, 30, 31, 32, 33, 34, 35},{23, 24, 25, 26, 27, 28, 
29, 30, 31, 32, 33, 34, 35}}

EDIT: With @ciao's help, I have the solution

EDIT 2: Fidgeting around for a bit, I realized on dropping the outer Union, the problem is solved.

Producing

FinalList = {{23, 24, 25, 26}, {23, 24, 25, 26, 27, 28}, {23, 24, 25, 26, 27, 28, 
29}, {23, 24, 25, 26, 27, 28, 29, 30}, {23, 24, 25, 26, 27, 28, 29, 
30, 31, 32}, {23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33}, {23, 24, 
25, 26, 27, 28, 29, 30, 31, 32, 33, 35}, {23, 24, 25, 26, 27, 28, 
29, 30, 31, 32, 33, 34, 35},{23, 24, 25, 26, 27, 28, 
29, 30, 31, 32, 33, 34, 35}}

Edit

With @ciao's help, I have the solution

Edit 2

Fidgeting around for a bit, I realized on dropping the outer Union, the problem is solved.

8 deleted 7 characters in body
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I have a number of lists (only 3 shown here)

`

List1 = {{23, 24, 25, 26}, {23, 24, 25, 26, 27, 28}, {23, 24, 25, 26, 27, 28, 29}}
List2 = {{23, 24, 26, 30, 29}, {23, 24, 26, 29, 30, 31, 32}}
List3 = {{31, 33, 23}, {23, 31, 33, 35}, {23, 31, 33, 34, 35}, {23, 31, 33, 34, 35}}

I want to make a combine these lists in the following way: Union the last element of List1 with each element of List2, and add it to the end of List1, then Union the last element of List2 to all the elements of List3 and add them to the end of List1.

Producing

`

FinalList = {{23, 24, 25, 26}, {23, 24, 25, 26, 27, 28}, {23, 24, 25, 26, 27, 28, 
29}, {23, 24, 25, 26, 27, 28, 29, 30}, {23, 24, 25, 26, 27, 28, 29, 
30, 31, 32}, {23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33}, {23, 24, 
25, 26, 27, 28, 29, 30, 31, 32, 33, 35}, {23, 24, 25, 26, 27, 28, 
29, 30, 31, 32, 33, 34, 35},{23, 24, 25, 26, 27, 28, 
29, 30, 31, 32, 33, 34, 35}}

I should mention, the numbers are random, although here it appears as consecutive at some places.

EDIT: With @ciao's help, I have the solution

Union@FoldList[Union, Join[List1, List2, List3]]

However, it seems to drop repeated elements as it appears in List3.

EDIT 2: Fidgeting around for a bit, I realized on dropping the outer Union, the problem is solved.

FoldList[Union, Join[List1, List2, List3]]

I have a number of lists (only 3 shown here)

`

List1 = {{23, 24, 25, 26}, {23, 24, 25, 26, 27, 28}, {23, 24, 25, 26, 27, 28, 29}}
List2 = {{23, 24, 26, 30, 29}, {23, 24, 26, 29, 30, 31, 32}}
List3 = {{31, 33, 23}, {23, 31, 33, 35}, {23, 31, 33, 34, 35}, {23, 31, 33, 34, 35}}

I want to make a combine these lists in the following way: Union the last element of List1 with each element of List2, and add it to the end of List1, then Union the last element of List2 to all the elements of List3 and add them to the end of List1.

Producing

`

FinalList = {{23, 24, 25, 26}, {23, 24, 25, 26, 27, 28}, {23, 24, 25, 26, 27, 28, 
29}, {23, 24, 25, 26, 27, 28, 29, 30}, {23, 24, 25, 26, 27, 28, 29, 
30, 31, 32}, {23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33}, {23, 24, 
25, 26, 27, 28, 29, 30, 31, 32, 33, 35}, {23, 24, 25, 26, 27, 28, 
29, 30, 31, 32, 33, 34, 35},{23, 24, 25, 26, 27, 28, 
29, 30, 31, 32, 33, 34, 35}}

I should mention, the numbers are random, although here it appears as consecutive at some places.

EDIT: With @ciao's help, I have the solution

Union@FoldList[Union, Join[List1, List2, List3]]

However, it seems to drop repeated elements as it appears in List3.

EDIT 2: Fidgeting around for a bit, I realized on dropping the outer Union, the problem is solved.

FoldList[Union, Join[List1, List2, List3]]

I have a number of lists (only 3 shown here)

`

List1 = {{23, 24, 25, 26}, {23, 24, 25, 26, 27, 28}, {23, 24, 25, 26, 27, 28, 29}}
List2 = {{23, 24, 26, 30, 29}, {23, 24, 26, 29, 30, 31, 32}}
List3 = {{31, 33, 23}, {23, 31, 33, 35}, {23, 31, 33, 34, 35}, {23, 31, 33, 34, 35}}

I want to combine these lists in the following way: Union the last element of List1 with each element of List2, and add it to the end of List1, then Union the last element of List2 to all the elements of List3 and add them to the end of List1.

Producing

`

FinalList = {{23, 24, 25, 26}, {23, 24, 25, 26, 27, 28}, {23, 24, 25, 26, 27, 28, 
29}, {23, 24, 25, 26, 27, 28, 29, 30}, {23, 24, 25, 26, 27, 28, 29, 
30, 31, 32}, {23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33}, {23, 24, 
25, 26, 27, 28, 29, 30, 31, 32, 33, 35}, {23, 24, 25, 26, 27, 28, 
29, 30, 31, 32, 33, 34, 35},{23, 24, 25, 26, 27, 28, 
29, 30, 31, 32, 33, 34, 35}}

I should mention, the numbers are random, although here it appears as consecutive at some places.

EDIT: With @ciao's help, I have the solution

Union@FoldList[Union, Join[List1, List2, List3]]

However, it seems to drop repeated elements as it appears in List3.

EDIT 2: Fidgeting around for a bit, I realized on dropping the outer Union, the problem is solved.

FoldList[Union, Join[List1, List2, List3]]
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