Computer system at home managed to be overloaded with tweets, oddly (8)
I believe the answer is:
intranet
'computer system' is the definition.
(type of computer network)
'home managed to be overloaded with tweets oddly' is the wordplay.
'home' becomes 'in' ('he's home' can mean 'he's in').
'managed' becomes 'ran' (I've seen this in another clue).
'to be overloaded with' means one lot of letters goes inside another (some letters go around or over others).
'oddly' indicates alternate letters (letters in the odd-numbered positions are used).
The alternating letters of 'tweets' are 'tet'.
'ran' going within 'tet' is 'tranet'.
'in'+'tranet'='INTRANET'
'at' acts as a link.
(Other definitions for intranet that I've seen before include "Private electronic network" , "linked office computers" , "Company computer system" , "Private communications network" , "Website with restricted access" .)