The budget for the Health and Human Services Department would increase about $14 billion to $289 billion under President Reagan's fiscal 1984 budget.

Most of that, however, represents automatic increases in Social Security, Medicare and Medicaid, the entitlement programs that, with welfare, make up 96 percent of the HHS budget.

Many smaller programs, particularly in medical research and social services, would be cut or would receive tiny increases that would fail to keep pace with inflation.

The biggest changes would involve Social Security, where changes to speed up taxes and slow the growth of benefits were proposed with the recommendations of the bipartisan Social Security commission. Changes also were proposed in Medicare, primarily raising routine charges in exchange for protection against "catastrophic costs" when hospital stays exceed 60 days.

Among the other proposals:

* In Medicaid, the administration would like to charge patients $1 to $1.50 a visit for doctor care, and $1 or $2 per day in the hospital. For 1985, it wants Congress to reduce the federal matching payment to each state by 3 percent from the level before Reagan took office.

A reduced matching formula approved in 1981 is scheduled to expire in fiscal 1984. The 1984 federal outlays would be $20.8 billion; they would be $293 million more if the changes are not approved.

* The total number of employe work years would be cut by 4,100, to 137,900.

* The Public Health Service's funding would be cut from $7.795 billion in budget authority to $7.702 billion, largely through cuts in health planning and health professions training funds. Most other programs, including the Food and Drug Administration, Centers for Disease Control and National Institutes of Health, would increase slightly, but not enough to compensate for inflation.

Family planning would be merged into the primary care block grant, a controversial proposal unacceptable to Rep. Henry A. Waxman (D-Calif.), chairman of the House Energy and Commerce subcommittee on health.

* The budget for Supplemental Security Income, welfare for the aged, blind and disabled, would be $7.85 billion, including a six-month postponement of the cost-of-living adjustment. Recipients who also are on the Social Security rolls would get $30 a month more in basic benefits to compensate for certain losses they would suffer because of changes in Social Security.

* In welfare, Aid to Families with Dependent Children, outlays would come to $7.1 billion after $722 million in proposed benefit cuts including workfare and income adjustments.

* The administration proposed cutting household fuel subsidies to the poor to $1.3 billion, $686 million below the appropriation for 1983, and focusing on the coldest states with the most poor residents.

* Programs for the aged would be cut slightly; the Community Services and Social Services Block Grants, now totaling $2.8 billion combined, would be merged at $2.5 billion, and the existing $271 million work-incentive program to train and place welfare recipients would be eliminated.