Is it okay to delete MSDB?
You can't drop the msdb database as stated in the docs (emphasis mine):


  Restrictions
  
  The following operations cannot be performed on the msdb database:
  
  
  Changing collation. The default collation is the server collation.
  Dropping the database.
  Dropping the guest user from the database.
  Enabling change data capture.
  Participating in database mirroring.
  Removing the primary filegroup, primary data file, or log file.
  Renaming the database or primary filegroup.
  Setting the database to OFFLINE.
  Setting the primary filegroup to READ_ONLY.
  


Tampering with system databases isn't a good idea usually. You should check where your space problem is and consider expanding your drives.



To check where your size problem is:


Check table and index sizes inside msdb database using this query:

USE msdb
GO

SELECT 
    t.NAME AS TableName,
    s.Name AS SchemaName,
    p.rows AS RowCounts,
    SUM(a.total_pages) * 8 AS TotalSpaceKB, 
    CAST(ROUND(((SUM(a.total_pages) * 8) / 1024.00), 2) AS NUMERIC(36, 2)) AS TotalSpaceMB,
    SUM(a.used_pages) * 8 AS UsedSpaceKB, 
    CAST(ROUND(((SUM(a.used_pages) * 8) / 1024.00), 2) AS NUMERIC(36, 2)) AS UsedSpaceMB, 
    (SUM(a.total_pages) - SUM(a.used_pages)) * 8 AS UnusedSpaceKB,
    CAST(ROUND(((SUM(a.total_pages) - SUM(a.used_pages)) * 8) / 1024.00, 2) AS NUMERIC(36, 2)) AS UnusedSpaceMB
FROM 
    sys.tables t
INNER JOIN      
    sys.indexes i ON t.OBJECT_ID = i.object_id
INNER JOIN 
    sys.partitions p ON i.object_id = p.OBJECT_ID AND i.index_id = p.index_id
INNER JOIN 
    sys.allocation_units a ON p.partition_id = a.container_id
LEFT OUTER JOIN 
    sys.schemas s ON t.schema_id = s.schema_id
GROUP BY 
    t.Name, s.Name, p.Rows
ORDER BY 
    TotalSpaceMB DESC


If sysjobhistory pops up in space then review your current job history rentention policy and make sure that your jobs' schedules are on check and not triggering more often than they need.
Check database data and log file sizes with this query:

;with fs
as
(
    select database_id, type, size * 8.0 / 1024 size
    from sys.master_files
)
select
    name,
    (select sum(size) from fs where type = 0 and fs.database_id = db.database_id) DataFileSizeInMB,
    (select sum(size) from fs where type = 1 and fs.database_id = db.database_id) LogFileSizeInMB
from 
    sys.databases db
where
    db.name = 'msdb'


If the log file size is high you need to find out which operation made it increase it's size and troubleshoot it. Shrinking the file will free some space but won't solve the underlying problem.