Answer: To control lawn weeds you may need to try several approaches. In an area that small you could spot treat the individual weeds with an herbicide containing glyphosate or triclopyr. Be sure to read and carefully follow the directions for application and waiting period, and as to which specific weeds each one controls. Do not allow these herbicides to contact your flowers.
Alternatively you could hand dig them, being sure to take the entire root. With onion grass you need to take the main bulb and the baby bulbs beside it.
While you are working on weed control, do not allow the existing weeds to flower and set seed.
Correct mowing, pH and fertility can go a long way toward encouraging healthy turf grass that can crowd out weeds. Mow often enough that you never take off more than one third of the grass height at a time. This can mean mowing more than once a week in the spring.
Run some basic soil tests to check the fertility and verify how much fertilizer you need to use for turf grass. Also check the pH to see if you need to adjust it with lime. Finally, topdressing the lawn with good quality compost will help feed the soil and ultimately strengthen the lawn grass.
You may also want to do a core aeration to help reduce compaction.
Your local county extension should be able to help you with the tests and interpreting the results.
Grubs can be treated, if necessary, by applying beneficial nematodes. You would not treat for grubs unless you have a specific problem with them.
Q&A Library Searching Tips