select 
case when regexp_like('78+9','^\+{0,1}') then 1 else 0 end
from dual

select 
case when regexp_like('78+9','^ *\+{0,1}[[:digit:] ]*$') then 1 else 0 end res
from dual;

SQL> select 
  2  case when regexp_like('+','^ *\+{0,1}[[:digit:] ]*$') then 1 else 0 end res
  3  from dual;
       RES
----------
         1

SQL> select 
  2  case when regexp_like(null, '^ *\+{0,1}[[:digit:] ]*$') then 1 else 0 end res
  3  from dual;
       RES
----------
         0

SQL> select 
  2  case when regexp_like(nvl(null,' '), '^ *\+{0,1}[[:digit:] ]*$') then 1 else 0 end res
  3  from dual;
       RES
----------
         1

SQL> select 
  2  case when regexp_like(' ', '^ *\+{0,1}[[:digit:] ]*$') then 1 else 0 end res
  3  from dual;
       RES
----------
         1

SQL> with 
  2    data as (
  3      select '78+9' val from dual
  4      union all
  5      select '+789' from dual
  6      union all
  7      select '- 789' from dual
  8      union all
  9      select '0112 548 2135 ' from dual
 10      union all
 11      select '+' from dual
 12      union all
 13      select '-' from dual
 14      union all
 15      select null from dual
 16      union all
 17      select ' ' from dual
 18    )
 19  select '"'||val||'"' val, 
 20         case 
 21           when regexp_like(nvl(trim(val),'0'), '^ *[-\+]{0,1} *[[:digit:]][[:digit:] ]*$') 
 22             then 1 
 23           else 0 
 24         end res
 25  from data
 26  /
VAL                     RES
---------------- ----------
"78+9"                    0
"+789"                    1
"- 789"                   1
"0112 548 2135 "          1
"+"                       0
"-"                       0
""                        1
" "                       1

Don't assume - READ documentation. Asterisk is 0 or more occurrences.

{0,1} can be shortened with question mark.

[[:digit:] ]* means digit_or_space repeated 0_or_more_times. 
Therefore, null_or_bunch_of_spaces_without_any_digits fall under the pattern. Since 
your requirement is to have at least one digit Michel used [[:digit:]] [[:digit:]_]* 
which means digit followed by any number of_digits and/or spaces thus enforcing at 
least one digit. Btw, first [[:digit :]] can be shortened with \d and [[:digit:] ] 
with [0-9 ].

with 
    data as (
     select 0.0027 as val  from dual
      union all
      select 0.0068563 from dual
      union all
      select 0.007685 from dual
      union all
      select 0 from dual
    )
  select '"'||val||'"' val, 
         case 
           when regexp_like(nvl(trim(val),0), '^ *[-\+]{0,1}[[:digit:]]\.?[[:digit:]]*$') 
             then 1 
           else 0 
         end res
  from data

with data as (
select '020-7332-6474' as val from dual
union all
select '44(0)8709507900' from dual
union all
select '0033 (0) 240899432' from dual
union all
select '44 (0) 1483 452 622' from dual
union all
select '1(604) 592-2908' from dual
union all
select 'MOB (604) 592-2908' from dual
union all
select '+1(604)-592-2908' from dual
union all
select '06045922908' from dual
)

select ''''||val||'''' val,
case 
    when regexp_like(nvl(trim(val),'0'), '^\+?[[:digit:]]*[[\(\.-] ]?[:digit:]*[\)\.-] ]?[:digit:]*$') 
       then 1 
       else 0 
end res 
from data

with data as (
select '020-7332-6474' as val from dual
union all
select '44(0)8709507900' from dual
union all
select '0033 (0) 240899432' from dual
union all
select '44 (0) 1483 452 622' from dual
union all
select '1(604) 592-2908' from dual
union all
select 'MOB (604) 592-2908' from dual
union all
select '+1(604)-592-2908' from dual
union all
select '06045922908' from dual
)
select  ''''||val||'''' val,
        case
          when regexp_like(nvl(replace(val,' '),'0'),'^\+?\d*(\(\d+\))?(-?\d+)+$') then 1
          else 0
        end res
from data
/

VAL                          RES
--------------------- ----------
'020-7332-6474'                1
'44(0)8709507900'              1
'0033 (0) 240899432'           1
'44 (0) 1483 452 622'          1
'1(604) 592-2908'              1
'MOB (604) 592-2908'           0
'+1(604)-592-2908'             1
'06045922908'                  1

8 rows selected.

SQL>