A Quick Sudoklu

Across

 1. ?? P on a B B
2. a S in T S ?
3. ?? O in a P
4. as E as ???
6. ? T on a F
7. ?? I in a Y
9. ?? G S
11. ?? H in a D
12. ? B in a B
13. ? S to the W
14. ?? M of F
15. the ? B of M
16. a H Q D N and P is ?? C
17. a S S D has ?? P [or "a S S D has ?? D", or "a S S D has ?? S"]
18. the ? D S


Down

 1. ?? L in the E A
2. to G the W ? Y
3. to G B to S ?
4. a C has ?? E
5. ?? B K on a P
6. the ? P of I
7. ?? P in a G of C
8. ?? S on a C B
9. L ? P in a P
10. ?? R in a S of C
12. ? F in a M
13. ? is a C
14. ?? D in a F
15. ?? W in a Y
16. on C ?
18. the ? Y I


Here is a text only version of the image for any who want one (clue numbers are right aligned while unnumbered unfilled clue squares are ?):

   1 2 3   4 5 6   7 8 9
+-------+-------+-------+
A| · · · | · · · | · 1 ? |A
B| · 2 · | · · · | 3 ? · |B
C| · · · | 4 ? 5 | · · · |C
+-------+-------+-------+
D| · · · | ? · ? | · · 6 |D
E| 7 8 · | · · · | 910 · |E
F|11 ? · | 12· · | · ? · |F
+-------+-------+-------+
G| · ·13 | ·14 ? | · · · |G
H| ·15 · | · ? · | ·16 ? |H
J| ·17 ? | · · · |18 · · |J
+-------+-------+-------+
1 2 3   4 5 6   7 8 9

• Note to others: I assume the letters are abbreviations, for example 15 down might be 52 weeks in a year. But I have nowhere near enough to post as an answer – Quintec Oct 22 '18 at 0:42
• @JonathanAllen Would I be right in thinking that there might be at least one "of" or similar little word omitted from 17a for the sake of symmetry? – Gareth McCaughan Oct 22 '18 at 1:09
• (I think I have nearly all of them, but "nearly all of them" is not nearly enough to allow you to deduce many other entries in the sudoku...) – Gareth McCaughan Oct 22 '18 at 1:12
• @GarethMcCaughan 17a has no missing word unless there's a wording I haven't thought about. – Jonathan Allan Oct 22 '18 at 5:56

(Credit where it's due: Thanks to @Stidgeon and @Reinier for pointing out in comments some answers I hadn't found.)

Across

1. ?? P on a B B <-- 24 points on a backgammon board
2. a S in T S ? <-- a stitch in time saves nine
3. ?? O in a P <-- 16 ounces in a pound
4. as E as ??? <-- as easy as 123
6. ? T on a F <-- 5 toes on a foot
7. ?? I in a Y <-- 36 inches in a yard
9. ?? G S <-- 21 gun salute
11. ?? H in a D <-- 24 hours in a day
12. ? B in a B <-- 8 bits in a byte
13. ? S to the W <-- 3 sheets to the wind
14. ?? M of F <-- 15 minutes of fame [thanks, @Reinier!] 15. the ? B of M <-- 5 books of Moses
16. a H Q D N and P is ?? C <-- a half, quarter, dollar, and nickel is 91 cents
17. _a S S D has ?? P/D/S <-- a six-sided die has 21 pips, dots, or spots [thanks to Stidgeon for spotting that we only needed to vary the last word]
18. the ? D S <-- 7 deadly sins

Down

1. ?? L in the E A <-- 26 letters in the English alphabet
2. to G the W ? Y <-- to go the whole 9 yards
3. to G B to S ? <-- to go back to square 1
4. a C has ?? E <-- a cube has 12 edges
5. ?? B K on a P <-- 36 black keys on a piano
6. the ? P of I <-- 5 pillars of Islam
7. ?? P in a G of C <-- 32 pieces in a game of chess
8. ?? S on a C B <-- 64 squares on a chess board
9. L ? P in a P <-- like 2 peas in a pod
10. ?? R in a S of C <-- 13 ranks in a suit of cards [thanks, @Reinier!] 12. ? F in a M <-- 8 furlongs in a mile [thanks, @Stidgeon!] 13. ? is a C <-- 3 is a crowd
14. ?? D in a F <-- 14 days in a fortnight
15. ?? W in a Y <-- 52 weeks in a year
16. on C ? <-- on cloud 9
18. the ? Y I <-- the 7 year itch

and then the sudoku solves as follows:

1 2 3 4 5 6 7 8 9 +-------+-------+-------+ A| 1 3 7 | 5 6 9 | 8 2 4 |A B| 5 9 2 | 4 8 7 | 1 6 3 |B C| 6 8 4 | 1 2 3 | 5 7 9 |C +-------+-------+-------+ D| 7 1 8 | 2 3 6 | 9 4 5 |D E| 3 6 5 | 9 7 4 | 2 1 8 |E F| 2 4 9 | 8 5 1 | 6 3 7 |F +-------+-------+-------+ G| 9 7 3 | 6 1 5 | 4 8 2 |G H| 8 5 6 | 7 4 2 | 3 9 1 |H J| 4 2 1 | 3 9 8 | 7 5 6 |J +-------+-------+-------+ 1 2 3 4 5 6 7 8 9`

Minor loose end:

I haven't figured out all three of the SSD=21 ones. The first is clearly the number of pips on a six-sided die or a single standard die. The second is presumably something like the number of dominoes in a standard set of dominoes except that that requires an extra "of" which I'm assured isn't needed. And I don't know what the third one is, though I expect that like the other two it's a game-like thing and derived from 1+2+3+4+5+6.

• 17 across: (ROT13) N fvk fvqrq qvr unf 21 cvcf/qbgf/fcbgf – Stidgeon Oct 22 '18 at 3:31
• 12 down is 8 (ROT13) Sheybatf va n zvyr – Stidgeon Oct 22 '18 at 3:35
• You really are nearly there! – Jonathan Allan Oct 22 '18 at 5:58
• 14a: (ROT13) 15 zvahgrf bs snzr – Reinier Oct 22 '18 at 9:49
• 10d: (ROT13) 13 enaxf va n fhvg bs pneqf – Reinier Oct 22 '18 at 9:50