$x=4$ totalling 264 points averaging 5.28 points per target integer.
I've assumed that you don't have to use x if its not really needed. Otherwise the answer for 1 is 4/4 the answer for 2 is $\lfloor4-\phi\rfloor$ and the other 18 numbers that don't include x will need $\times4\div4$ appended increasing the total points to 339 for an average of 6.78 (although I might have another go at finding better answers for those 18 if they are inadmissible.)
$1= \lfloor \phi \rfloor$ (2 points)
$2=\lceil \phi \rceil$ (2 points)
$3=4-\lfloor \phi \rfloor $ (4 points)
$4=4 $ (1 point)
$5=4+\lceil \phi \rceil $ (4 points)
$6=\lfloor \phi \times 4 \rfloor$ (4 points)
$7=\lceil \phi \times 4\rceil$ (4 points)
$8=4 \times \lceil p\rceil $ (4 points)
$9=4+4+\lceil \phi \rceil $ (6 points)
$10=\lfloor 4 \times \phi \times \phi \rfloor$ (6 points)
$11=\lceil 4 \times \phi \times \phi \rceil $ (6 points)
$12=\lfloor \tau \times \lceil \phi \rceil \rfloor ($5 points)
$13=\lceil \tau \times \lceil \phi \rceil\rceil$ (5 points)
$14=4 \times 4- \lceil \phi \rceil $ (6 points)
$15=\lfloor \tau \times 4 \div \phi \rfloor $ (6 points)
$16=4 \times 4 $ (3 points)
$17=4 \times 4+\lfloor \phi \rfloor $ (6 points)
$18=\lfloor \tau \times 4 \div \phi + \phi \rfloor$ (8 points)
$19=\lfloor \phi + \phi +4 \times 4 \rfloor$ (8 points)
$20=\lfloor \phi ^t \rfloor $ (4 points)
$21=\lceil \phi ^ \tau \rceil $ (4 points)
$22=\lceil \phi + \phi ^ \tau \rceil $ (6 points)
$23=\lceil \phi + \phi ^ \tau \rceil $ (6 points)
$24=4! $ (2 points)
$25=\lfloor \tau \times 4 \rfloor$ (4 points)
$26=\lceil \tau \times 4 \rceil$ (4 points)
$27=\lceil \tau \times 4+ \phi \rceil$ (6 points)
$28=4 \times \lceil \phi \times 4 \rceil$ (6 points)
$29=\lfloor \phi +4 \times \phi ^4 \rfloor$ (8 points)
$30=\lfloor 4^{4\div\phi}\rfloor$ ( 6 points)
$31=\lceil 4^{4\div \phi }\rceil$ (6 points)
$32=4 \times 4 \times \lceil \phi \rceil$ (6 points)
$33=\lfloor \phi \times \phi ^ \tau \rfloor $ (6 points)
$34=\lceil \phi \times \phi ^ \tau \rceil$ (6 points)
$35=\lceil \phi + \phi \times \phi ^ \tau \rceil$ (8 points)
$36=\lfloor (4!- \phi ) \times \phi \rfloor$ (8 points)
$37=\lceil (4!- \phi ) \times \phi \rceil$ (8 points)
$38=\lfloor (4+4+ \phi ) \times 4 \rfloor$ (9 points)
$39=\lfloor \tau \times \tau \rfloor $ ( 4 points)
$40=\lceil \tau \times \tau \rceil $ (4 points)
$41=\lceil 4 \times \tau \times \phi \rceil $ (6 points)
$42=\lceil \phi \times \phi \times 4 \times 4 \rceil$ ( 8 points)
$43=\lfloor \phi ^{ \phi + \tau }- \phi \rfloor$ ( 6 points)
$44=\lfloor \phi ^{ \phi + \tau }\rfloor$ ( 6 points)
$45=\lceil \phi ^{ \phi + \tau }\rceil $ ( 6 points)
$46=\lfloor \phi + \phi ^{ \phi + \tau }\rfloor $ ( 8 points)
$47=\lceil \phi + \phi ^{ \phi + \tau }\rceil $ ( 8 points)
$48=\lfloor \phi + \phi + \phi ^{ \phi + \tau }\rfloor$ ( 10 points)
$49=\lceil \phi + \phi + \phi ^{ \phi + \tau }\rceil$ ( 10 points)
$50=\lfloor 4 \times \tau \times \lceil \phi \rceil\rfloor$ ( 7 points)