I traveled to Schengen country illegally as (Asylum seeker), now the host country gave me a temporary residence permit, If I can work in host country, so can I work outside the host country mean in other Schengen country like Germany? Can I travel in the Schengen area after acquiring my temporary residence permit from host country?
Residence permit holders can generally travel in Schengen freely. From the Citizens Information site of Ireland:
If you have a valid residence permit in one Schengen country you can travel to the others without needing a visa (in effect, a residence permit from a Schengen country is the same as a Schengen visa).
However, asylum seekers generally may not travel or work outside the host country:
Asylum seekers in one participating country are not entitled to travel freely to another. They are subject to the rules set out in the Dublin Convention on the country to which their application for asylum must be made.
So it's going to depend on what exactly your "temporary residence permit" is. If it has no conditions attached, you should be free to travel; if it's only until your asylum application has been processed, you may not travel. Ask the authorities who issued it.
For what it's worth, the europa.eu page on the Dublin II Regulation does not mention this explicitly, but the travel ban appears to be a side effect of the rule forbidding asylum seekers from trying their luck in multiple countries.